The demolition of Masjid al-Dirar took place as a consequence of the people who built it, were hypocrites of the highest degree. They were the same people who waged war against Muslims before and continued plotting. This time round when they built the Masjid (Mosque) under the command of Abu Amr (Amir), they were helping the enemy, Byzantine Roman Empire to fight against the Muslims.
Hence, it was decided by the Prophet (p) to demolish this place of mischief so they can no longer make plans to attack the Muslims.
“The Messenger of God proceeded until he halted in Dhu Awan, a town an hour’s daytime journey from Medina. The people who had built the Mosque of dissent (Masjid al-Dirar) had come to him while he was preparing for Tabuk, saying,
‘O Messenger of God, we have built a mosque for the sick and needy and for rainy and cold nights, and we would like you to visit us and pray for us in it.’ [The Prophet] said that he was on the verge of travelling, and was preoccupied, or words to that effect, and that when he returned, God willing, he would come to them and pray for them in it.
When he stopped in Dhu Awan, news of the mosque came to him, and he summoned Malik b. Dukhshum, a brother of the Banu Salim, b. Awf, and Ma’n b. Adi, or his brother Asim b. b. Adi, brothers of the Banu al-Ajlan, and said,
‘Go to this mosque whose owners are unjust people and destroy and burn it.’ They went out briskly until they came to the Banu Salim b. Awf who were malik b. Al-Dukhsum’s clan. Malik said to Ma’n,
‘Wait for me until I bring fire from my people.’
He went to his kinsfolk and took a palm branch and lighted it. Then both of them ran until they entered the mosque, its people inside, set fire to it and destroyed it and the people dispersed.
Concerning them it was revealed in the Qur’an:
‘And those who have taken a mosque for [working] mischief and disbelief, as well as disunion among the faithful and as an outpost for those who already fought God and His Messenger, will swear, ‘we desired nothing but good.’ God witnesses what sort of liars they are.’ – Qur’an 9:107″ 
“The Prophet had received information which made him suspect the ulterior motives of the builders of this mosque. They were linked to those who had planned an attempt on the Prophet’s life when he was returning from Tabuk. … They were acting in concert with Abu Amir, an opponent of the Prophet. …” (Tafsir al-Tabari, volume 14, page 469 – 475) 
THE DIRAR MOSQUE
The hypocrites were always planning to create dissensions amongst the Muslims. They had long been scheming to erect at this place a mosque, to rival that of Quba. Their pretet was that the People, who were unable to go to the Prophet’s mosque owing to their infirmity or for any other reason, might say their prayers there. ABU AMIR, a Medinite, who had turned Christian, had asked the Hypocrites to start their preparations AS HE WAS GOING TO ASK HERACLEUS FOR MILITARY AID, SO THAT THE COUNTRY MIGHT BE PURGED OF ISLAM. (Zurqani, volume 3, page 91) (Sirat-Un-Nabi (‘The Life Of The Prophet’] [Rendered Into English by M. Tayyib Bakhsh Budayuni – Idarah-I Adabiyati-I Delli, 2009 Qasimjan St, Delhi (India), 1983] by Allama Sibli Nu’mani, volume 2, page 238 – 239)
“And, among them, those who have chosen a mosque — these were twelve men from among the hypocrites — by way of harm, to cause distress for those of the mosque of Quba’, and disbelief, since they built it on the orders of the monk Abu ‘Amir, as a sanctuary for him, so that whoever comes from his side may stay there: he had gone to the Byzantine Emperor (qaysar) to bring troops to fight against the Prophet (s), and to cause division among the believers, who pray in the mosque of Quba’, by having some of these pray in their [the hypocrites’] mosque, and as an outpost, an observation post, for those who waged war against God and His Messenger before, that is, before it was built — meaning the above-mentioned Abu ‘Amir — they will swear: ‘We desired nothing, by building it, but, to do, good’, by way of kindness towards the poor in times of [heavy] rain or [extreme] heat and in order to provide [a place of worship] for the Muslims; and God bears witness that they are truly liars, in this [claim of theirs]. They had asked the Prophet (s) to perform prayers in it, and so the following was revealed:” 
Asbab Al-Nuzul by Al-Wahidi:
“(And as for those who chose a place of worship out of opposition and disbelief, and in order to cause dissent among the believers, and as an outpost for those who warred against Allah and His messenger aforetime, they will surely swear: We purposed naught save good. Allah beareth witness that they verily are liars. Never stand (to pray) there…) [9:107-108]. The commentators of the Qur’an said: “The Banu ‘Amr ibn ‘Awf built a mosque at Quba’ and sent for the Messenger of Allah, to come to them. He went there and prayed in that mosque. Their brothers from the Banu Ghunm ibn ‘Awf envied them resentfully and said: ‘Let us built a mosque and send for the Messenger of Allah, to pray in it as he prayed in the mosque of our brothers, and let Abu ‘Amir al-Rahib (the monk) also pray in it when he comes back from Syria‘. This Abu ‘Amir had embraced Christianity and became a monk in the pre-Islamic period. But when the Messenger of Allah, moved to Medina, Abu ‘Amir rejected the religion of Islam and showed enmity toward it. The Prophet, called him then Abu ‘Amir al-Fasiq (the corrupt) [instead of Abu ‘Amir al-Rahib (the monk)]. Abu ‘Amir left to Syria and then sent a letter to the hypocrites in which he wrote: ‘Prepare yourselves and make ready whatever you can of force and weapons. Built a mosque for me, for I am going to the Caesar to request him to send with me Byzantine soldiers so that I drive out Muhammad and his Companions‘. And so, they built for him a mosque by the Quba’ mosque. Those who built this mosque were 12 men: Khidham ibn Khalid (this mosque of opposition was an extension of his house), Tha’labah ibn Hatib, Mu’attib ibn Qushayr, Abu Habibah ibn al-Az’ar, ‘Abbad ibn Hunayf, Jariyah ibn ‘Amir, his two sons Majma’ and Zayd, Nabtal ibn Harith, Bahzaj ibn ‘Uthman, Bijad ibn ‘Uthman and Wadi’ah ibn Thabit. When they finished building this mosque, they went to the Messenger of Allah, and said: ‘We have built a mosque for the sick and the needy and also for use in rainy and wintry nights, and we would like you to come and pray in it’.” 
Tafsir Ibn Kathir:
“Masjid Ad-Dirar and Masjid At-Taqwa
The reason behind revealing these honorable Ayat is that before the Messenger of Allah migrated to Al-Madinah, there was a man from Al-Khazraj called “Abu `Amir Ar-Rahib (the Monk).” This man embraced Christianity before Islam and read the Scriptures. During the time of Jahiliyyah, Abu Amir was known for being a worshipper and being a notable person among Al-Khazraj. When the Messenger of Allah arrived at Al-Madinah after the Hijrah, the Muslims gathered around him and the word of Islam was triumphant on the day of Badr, causing Abu `Amir, the cursed one, to choke on his own saliva and announce his enmity to Islam. He fled from Al-Madinah to the idolators of Quraysh in Makkah to support them in the war against the Messenger of Allah. The Quraysh united their forces and the bedouins who joined them for the battle of Uhud, during which Allah tested the Muslims, but the good end is always for the pious and righteous people. The rebellious Abu Amir dug many holes in the ground between the two camps, into one of which the Messenger fell, injuring his face and breaking one of his right lower teeth. He also sustained a head injury. Before the fighting started, Abu Amir approached his people among the Ansar and tried to convince them to support and agree with him. When they recognized him, they said, “May Allah never burden an eye by seeing you, O Fasiq one, O enemy of Allah!” They cursed him and he went back declaring, “By Allah! Evil has touched my people after I left.” The Messenger of Allah called Abu Amir to Allah and recited the Qur’an to him before his flight to Makkah, but he refused to embrace Islam and rebelled. The Messenger invoked Allah that Abu Amir die as an outcast in an alien land, and his invocation came true. After the battle of Uhud was finished, Abu Amir realized that the Messenger’s call was still rising and gaining momentum, so he went to Heraclius, the emperor of Rome, asking for his aid against the Prophet. Heraclius gave him promises and Abu Amir remained with him. He also wrote to several of his people in Al-Madinah, who embraced hypocrisy, promising and insinuating to them that he will lead an army to fight the Messenger of Allah to defeat him and his call. He ordered them to establish a stronghold where he could send his emissaries and to serve as an outpost when he joins them later on. These hypocrites built a Masjid next to the Masjid in Quba’, and they finished building it before the Messenger went to Tabuk. They went to the Messenger inviting him to pray in their Masjid so that it would be a proof that the Messenger approved of their Masjid.” 
Tafsir Ibn Juzayy:
“… (to create division between the muminun) They meant to separate the believers from the Mosque of Quba’. (and in readiness for those who previously made war on Allah and His Messenger ) i.e. waiting for the one who fighs Allah and His Messenger. He was Abu ‘Amir ar-Rahib who the Messenger of Allah called a fasiq. He was one of the people of Madina. When the Messenger of Allah came to Madina, he fought with rejection and hyprocrisy, and then left for Makka and formed the parties of the idolaters. When Makka was conquered, he went to Ta’if. When the people of Ta’if became Muslim, he went to Syria and sought the help of Caesar. He died there. The people of the Mosque of Harm said, “When Abu ‘Amir came to Madina, he prayed in this mosque.” “Before” indicates what he did with the Parties.” 
Dr. Shawqi Abu Khalil:
“Then in the year 9 H, just before the Battle of Tabuk, a group of 12 hypocrites built Masjid Dirar (mosque of hypocrites), the purpose of which was to promote harm and disbelief, and to disunite the believers. They asked the Prophet to pray in their Masjid, and he answered,
‘Indeed, I am upon a journey (for the battle of Tabuk) and am much occupied, had we approached [there], we would have come to you and prayed in it.’” 
Hajjah Amina Adil:
The hypocrites endeavoured to vail themselves of every opportunity to create discord, and when they failed in sowing strife within the family, they tried to turn the Muslims against one another. To this aim, they decided to erect a new mosque opposite of the Prophet’s mosque at Quba. Their pretence was that the sick and elderly should find therein a place for prayer and refuge, but in reality they built it to split the Muslim community of Quba. Behind this plan was the infamous villain Abu Amir who urged his men, on, saying, ‘Go ahead, start building the mosque and see to it that as much weaponry as possible is hidden and stored in it.” 
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 The History of al-Tabari:The Last Years of the Prophet: the Formation of the State A.D. 630-632/A.H. 8-11: by Abu Ja’far Muhammad Bin Jarir Al-Tabari (Author), Ismail K. Poonawala (Translator), volume 9, page 60 – 61
 The History of al-Tabari:The Last Years of the Prophet: the Formation of the State A.D. 630-632/A.H. 8-11: by Abu Ja’far Muhammad Bin Jarir Al-Tabari (Author), Ismail K. Poonawala (Translator), volume 9, page 61 [FOOTNOTES section pg. 61]
 Tafsir al-Jalalayn http://altafsir.com/Tafasir.asp?tMadhNo=0&tTafsirNo=74&tSoraNo=9&tAyahNo=107&tDisplay=yes&UserProfile=0&LanguageId=2
 Asbab Al-Nuzul by Al-Wahidi http://altafsir.com/Tafasir.asp?tMadhNo=0&tTafsirNo=86&tSoraNo=9&tAyahNo=107&tDisplay=yes&UserProfile=0&LanguageId=2
 Tafsir Ibn Kathir: http://www.qtafsir.com/index.php?option=com_content&task=view&id=1590&Itemid=64
 Tafsir Ibn Juzayy: https://bewley.virtualave.net/tawba4.html
 Atlas Al-sirah Al-Nabawiyah – Atlas On The Prophet’s Biography Places, Nations, Landmarks, By Dr. Shawqi Abu Khalil, Page 235
 Muhammad, the Messenger of Islam: His Life & Prophecy, By Hajjah Amina Adil, page 538