Occasionally, we have to cull an animal that we weren’t prepared to cull. We always try to have a refrigerator in the garage for aging meats. This is needed for this eventuality too.
If an animal is in too much pain from an injury, we won’t let it suffer but we need it to die as quickly and painlessly as possible. A sharp knife across the jugular is the cleanest, quickest way to do this for most animals (except for pigs). They will bleed out in seconds and the pain is minimal.