Sayyiduna Adi bin Hatim (may Allah be pleased with him) says: I asked the Messenger of Allah (peace and blessings be upon him) about an arrow that strikes game with its broad side, and he (peace and blessings be upon him) said: "When the arrow strikes the game with its edge, eat; and when the arrow strikes with its broad side and kills the game, it will be regarded as having died from the blow of a piece of wood, so do not eat that game." The narrator says: What if I send my dog? He said: "When you send your dog after game, say 'Bismillah' (In the name of Allah) and 'Allahu akbar' (Allah is the Greatest), then eat." The narrator says: What if the dog has eaten from it? He said: "Then do not eat, for it has hunted for itself, not for you." The narrator says: What if I find other dogs with my dog? He said: "Then do not eat, for you mentioned the name of Allah over your own dog, not over the other dog."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيد والذبائح / 18872