1. Literally, to force the head off of a person or animal with a sudden, forceful, violent motion. I stood horrified when he picked the poor animal up and snapped its head off. I remember being traumatized after seeing a movie as a kid where a giant snaps a man's head off.

2. To respond to someone with extreme and sudden anger. What's wrong with the boss today? I just tried to ask him a question, and he totally snapped my head off! The teacher snapped Billy's head off for talking during class again.