Permission to hamstring the mount of an enemy during battle

Imam al-Shafi'i (may Allah have mercy on him) says that Hanzalah bin al-Rahib (may Allah be pleased with him) hamstrung the mount of Abu Sufyan bin Harb (may Allah be pleased with him) on the day of Uhud. His horse sank down, and Abu Sufyan (may Allah be pleased with him) fell; then Hanzalah (may Allah be pleased with him) sat on his chest to slaughter him. Ibn Sha'ub saw it, rushed at him like a beast of prey and killed him, and rescued Abu Sufyan (may Allah be pleased with him) from beneath him. After that Abu Sufyan (may Allah be pleased with him) recited these verses:
Had I wished, a strong bay-black horse would have saved me, and I would not have had to bear the favour of Ibn Sha'ub. My colt kept driving off their dog from early morning until it was near sunset. I will keep fighting them, and I will call out: Come to Ghalib!, and I will keep repelling them from myself with the might of the cross.

Ibn Ishaq narrates from al-Zuhri and others concerning the story of Uhud. He mentioned the story of Hanzalah (may Allah be pleased with him) with Abu Sufyan (may Allah be pleased with him), Ibn Sha'ub's helping Abu Sufyan (may Allah be pleased with him), and the killing of Hanzalah (may Allah be pleased with him), but he did not mention the hamstringing. Then he mentioned the verses of Abu Sufyan (may Allah be pleased with him) as Imam al-Shafi'i (may Allah have mercy on him) related them, though he also added to them.
Ibn Ishaq (may Allah have mercy on him) says: The name of Ibn Sha'ub was Shaddad bin al-Aswad. Al-Waqidi related concerning this story that he hamstrung his horse.

Muhammad bin Umar al-Waqidi (may Allah have mercy on him) narrates from his teachers, who mentioned the story of Hanzalah. They say: Hanzalah bin Abi Amir (may Allah be pleased with him) took up his weapons and joined the Messenger of Allah (peace and blessings be upon him) at Uhud, at the time when he (peace and blessings be upon him) was straightening the ranks. When the idolaters were routed, Hanzalah (may Allah be pleased with him) intercepted Abu Sufyan and cut the hamstring of his horse, so the horse sank down and Abu Sufyan fell to the ground. Abu Sufyan was shouting: O people of Quraysh! I am Abu Sufyan bin Harb! And Hanzalah (may Allah be pleased with him) wanted to slaughter him with the sword. Several men heard his voice, but because of the defeat no one paid any attention to him, until al-Aswad bin Sha'ub came to his aid. He charged at Hanzalah (may Allah be pleased with him) with a spear and ran him through, and Abu Sufyan fled.

Iyas bin Salamah narrates from his father (Sayyiduna Salamah bin al-Akwa' (may Allah be pleased with him)). He mentioned the story of al-Hudaybiyah and the return to Madinah, (saying) that the Messenger of Allah (peace and blessings be upon him) sent some camels with his servant Rabah (may Allah be pleased with him). The narrator says: I also went out with him, riding the horse of Sayyiduna Talhah (may Allah be pleased with him), and I too was looking after the camels. Suddenly, in the morning, Abd al-Rahman bin Uyaynah raided the camels of the Messenger of Allah (peace and blessings be upon him), drove them all away and killed the herdsman. I said: "O Rabah! Take this horse and give it to Sayyiduna Talhah bin Ubaydullah (may Allah be pleased with him), and go and inform the Messenger of Allah (peace and blessings be upon him) that the idolaters have raided the livestock." Then I climbed a hillock, faced Madinah and called out three times: "Ya sabahah, ya sabahah, ya sabahah!" (O the morning raid!) O people, we have been plundered this morning! Then I went after those people, shooting arrows at them and reciting verses: "Ana Ibn al-Akwa', wal-yawmu yawmu al-rudda'" (I am the son of al-Akwa', and today is the day the base ones perish). He says: I would shoot at a man and place the arrow so that it struck his shoulder, and then I would say: "Take this! Ana Ibn al-Akwa', wal-yawmu yawmu al-rudda'" (I am the son of al-Akwa', and today is the day the base ones perish). He says: I kept shooting at them and wounding them. Whenever a horseman turned back towards me, I would sit down behind a tree and shoot and wound him; and whenever the mountain pass narrowed, I would climb the mountain and rain stones on them. He says: I kept doing this until I had secured behind me every camel the Messenger of Allah (peace and blessings be upon him) had, and they left them to me. He mentioned the hadith, (until he said): I stayed in my place until I saw the horsemen of the Messenger of Allah (peace and blessings be upon him) emerging from among the trees. The first to arrive was Sayyiduna al-Akhram al-Asadi (may Allah be pleased with him), behind him Sayyiduna Abu Qatadah al-Ansari (may Allah be pleased with him), and after him Sayyiduna al-Miqdad bin al-Aswad al-Kindi (may Allah be pleased with him). I took hold of the reins of Sayyiduna al-Akhram's (may Allah be pleased with him) horse and said: "O Akhram! These people are few; beware of them, lest they destroy you, until the Messenger of Allah (peace and blessings be upon him) and his (peace and blessings be upon him) Companions (may Allah be pleased with them) reach us." He said: "O Salamah! If you believe in Allah and the Last Day and hold that Paradise and Hell are true, then do not stand between me and martyrdom." So I let him go. He met Abd al-Rahman bin Uyaynah, and Sayyiduna al-Akhram (may Allah be pleased with him) hamstrung Abd al-Rahman bin Uyaynah's horse; then Abd al-Rahman struck Sayyiduna al-Akhram (may Allah be pleased with him) with his spear and martyred him, and Abd al-Rahman mounted (Sayyiduna al-Akhram's) horse. Then Sayyiduna Abu Qatadah (may Allah be pleased with him) caught up with Abd al-Rahman and speared him, killing him; Abd al-Rahman had hamstrung his horse. Then Sayyiduna Abu Qatadah (may Allah be pleased with him) took Sayyiduna al-Akhram's (may Allah be pleased with him) horse, and they (the raiders) fled.