A lady slaughtered a sheep with a stone and then the Prophet (ﷺ) was asked about it and he permitted it to be eaten.
Sahih al-Bukhari Book 72, Hadith 30
← Previous Hadith that he said, "O Allah's Messenger (ﷺ)! We have no knife." The Prophet (ﷺ) said, "if the killing tool causes blood to gush out, and if Allah's Name is mentioned, eat (of the slaughtered animal). But do not slaughter with a nail or a tooth, for the nail is the knife of Ethiopians and a tooth is a bone." Suddenly a camel ran away and it was stopped (with an arrow). The Prophet (ﷺ) then said, "Of these camels there are some which are as wild as wild beasts; so if one of them runs away from you and you cannot catch it, treat it in this manner (i.e. shoot it with an arrow).

Sahih al-Bukhari Book 72, Hadith 29 Next Hadith → A slave girl belonging to Ka`b used to graze some sheep at Sl'a (mountain). Once one of her sheep was dying. She reached it (before it died) and slaughtered it with a stone. The Prophet (ﷺ) was asked, and he said, "Eat it."

Sahih al-Bukhari Book 72, Hadith 31