Sayyiduna Abu Tha'labah (may Allah be pleased with him) said: I came to the Messenger of Allah (peace and blessings be upon him), and he (peace and blessings be upon him) said: "As for what you mentioned, that you live in a land of game: whatever your bow strikes, mention the name of Allah over it, then eat."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيد والذبائح / 18939
Masruq narrates from Sayyiduna Abdullah (may Allah be pleased with him): "When you shoot game and it falls from a mountain and dies, do not eat it, for it may have died because of the fall; and if it falls into water and dies, do not eat it either, for it may have been killed by the water."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيد والذبائح / 18940