Another story circulated by critics is that of Abu Afak. It is claimed that the Prophet had him assassinated for merely writing some annoying poetry on the Prophet (p). Hence, the Prophet (p) got him killed. Let’s see if there is any truth to this. It is reported in Ibn Sa’d’s – Tabaqat al-Kabir the following:
Then (occurred) the Sariyyah of Salim Ibn Umayr al-Amri against Abu Afak, the Jew, in Shawaal in the beginning of the twentieth month from the hijrah of the Apostle. Abu Afak was from Banu Amr Ibn Awf… He was a Jew, and used to instigate the people against the Apostle of Allah. … 
In the above it said that Abu Afak was killed because he instigated people to go to war with Prophet Muhammed (p). Hence, one of the companions of the Prophet killed him. He being killed was not because he wrote annoying poetry on the Prophet – rather because he incited people to go to war against Muhammed (p). Furthermore, we have to be cautious with this story, it was said from scholars that the story on Abu Afak as a whole is forgery and as such it never occurred.
It is related that Abu Afak of Bani Amr had enraged the Moslems by fomenting enmity and sedition against their Government, when one Haris was executed for his murdering treacherously his fellow-comrade in the battle of Ohad during the time they were fighting together side by side. A convert from amongst the Bani Amr vowed to slay Abu Afak, and falling unawares upon him killed him with a cruel blow of his word. From Ibn Ishak we learn that Mohammad had said with reference to Abu Afak, ‘Who would rid me of this pestilent fellow?’ The biographers do not give their authorities whence they derived their information of the words attributed to Mohammad which he is said to have uttered with relation to Abu Afak before his followers; while at the same time it is no fair justice to form a hasty opinion of the fact without a critical examination and well-balancing of evidences of men like Ibn Ishak and others who have forgotten to tell us the original sources of their own assertion. Besides, the words quoted above are not equivalent to a peremptory order, and even granting this last condition, we are not justified in constructing them to mean assassination. Sir W. Muir writes that, ‘the secretary of Wackidi says distinctly-‘Now this was by command of the Prophet.’ (Vol. III, p. 133, f.n.). But it is a very easy thing for the secretary or other biographers to give an ample play to their fancies, or to fabricate commands, which the Prophet had never given out, on a very slender basis, or on no reasonable basis at all. The tendency of the biographers is always to exonerate the companions of the Prophet at the expense of truth, and to justify their deeds by casting the whole blame upon him. 
Maulana Muhammad Ali:
The next incident related… is that… to the alleged assassination of Abu Afak, ‘an aged Jewish proselyte, whose offence was similar to that of Asma.’ We have no hesitation in calling this story as baseless a fabrication as that relating to the murder of Asma. Our reason for doing this is that the interdiction against the murder of women also included two other classes, viz., children and old men. It is true that the saying of the Prophet in the Bukhari mentions only women and children, and not aged persons, but there is a hadith in Abu Dawud (ch. Du’a al-Mushrikin) reported by Anas, son of Malik, according to which the Holy Prophet said: ‘Do not kill an aged person, nor a child, nor a minor, nor a woman.’ That the Prophet expressly forbade the killing of old men appears also from the directions given by Abu Bakr, the first Caliph, to Yazid, son of Abu Sufyan, when he sent him in command of an army to Syria. In the directions given to him the following relates to our subject: ‘Do not kill children, nor women, nor old men.’ (Fath al-Qadir, vol V, p.202.) It is clear that Abu Bakr could give such directions only on the authority of the Holy Prophet. Hence there was an interdiction against the killing of old men as there was against the killing of women. And it is impossible, we repeat, that the Holy Prophet should have given such clear injunctions and then himself ordered the killing of ‘an aged Jewish proselyte,’ as Abu Afak is said to have been, and for no offence but that he composed some annoying verses.
ONLY COMBATANTS COULD BE KILLED
In fact, as the Hidayah has put it clearly, a person’s life, unless he is a murdered, cannot be taken on any ground other than that he is a combatant: ‘And they should not kill a woman, nor a child, nor an aged person, nor one who does not take part in a war, nor a blind man, because what makes it lawful to take a man’s life, according to us, is his being a Combatant, and this is not true in their cases’ (Ch. Kaifiyyat al-Qital). In fact, this conclusion, which is the basic principal of the Hanifite law, is based on the express words of the Holy Prophet himself. As Abu Dawud reports on the authority of Rabah, son of Rabi: ‘We were with the Prophet in a certain battle, and he saw the people gather together in one place. So he sent a man to make an inquiry as to why the people had gathered together. The messenger came back and said, ‘there is a woman killed.’ The Holy prophet said, ‘she was not fighting.’ The reporter says that Khalid was leading at the time. So the Prophet sent a man to Khalid and asked him to tell Khalid that he should not kill a woman nor a hireling’. (Ch. Qatl al-Nisa). By remarking that ‘she was not fighting’, the Holy Prophet made it plain that even in battle only such persons could be killed as actually took part in fighting, and along with women he expected hirelings, because they were only hired for other work and did not take part in actual fighting. It is on this basis that the Hanifite law excepts, along with women, children and old men, all such persons as cannot take part in fighting. And the conclusion is inevitable that according to the Holy Prophet’s own injunctions the killing of a person was not lawful unless he took part in fighting, and any report to the effect that a person was killed though he was not a combatant is either untrue or defective, even if it is met with in a reliable collection of traditions. And as for biographies, they cannot be trusted at all in such matters, and the case of Ibn Sunainah’s murder must be rejected as untrue. The statement that this murder was due to the Prophet giving a general order for the slaughter of the Jews is sufficient to discredit this report, for not only would such an order be against the clear injunctions of the Qur’an, but also because if such an order were given it would not have resulted in the murder of a single Jew. 
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 Ibn Sa’d – Tabaqat al-kabir, volume 2, page 31
 A Critical Exposition of the Popular Jihad (Original 1885) by Cherag Ali Page 64 – 65
 Muhammad The Prophet: By Maulana Muhammad Ali, page 201