Abu al-Ushara' al-Darimi narrates from his father (may Allah be pleased with him) that he said: "O Messenger of Allah (peace and blessings be upon him)! Is slaughter done only at the throat?" He (peace and blessings be upon him) said: "If you had struck it with a spear in its thigh, that too would have sufficed for you."
The Shaykh said: This applies to an animal that falls into a well and things similar to it.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصيد والذبائح / 18931