Mishkat al-Masabih #3929
Game and Animals Which May Be Slaughtered
The Arabic includes the chain of narration (sanad) and the collector's commentary; the English translation shows the Prophet's words only.
عَن أبي وَافد اللَّيْثِيّ قَالَ: قَدِمَ النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ الْمَدِينَةَ وَهُمْ يَجُبُّونَ أَسْنِمَةَ الْإِبِلِ وَيَقْطَعُونَ أَلْيَاتِ الْغَنَمِ فَقَالَ: «مَا يُقْطَعُ مِنَ الْبَهِيمَةِ وَهِيَ حَيَّةٌ فَهِيَ مَيْتَةٌ لَا تُؤْكَلُ» . رَوَاهُ التِّرْمِذِيُّ وَأَبُو دَاوُد
Abu Waqid al-Laithi told that when the Prophet came to Medina the people used to cut off camels' humps and cut the fat tails of sheep, so he said, “Whatever is cut off an animal when it is alive is dead* and must not be eaten.”
*i.e. it is treated as something which had died a natural death, and therefore may not be lawfully eaten.
Tirmidhi and Abu Dawud transmitted it.
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About Mishkat al-Masabih
This hadith is #3929 from Mishkat al-Masabih, in the Book of Game and Animals Which May Be Slaughtered.