The phrase conveys strong annoyance; use it to describe an overreaction rather than a calm reply. When he forgot to call her, she bit his head off.
Pro Tip 2/3
Informal Speech
It's colloquial and best used in casual conversations, not formal situations. If you ask about his ex, he might snap your head off.
Pro Tip 3/3
Not Literal
This is a metaphorical expression meaning no physical harm is done; it's about verbal reaction. Don't worry, she didn't actually bite my head off—it was just a figure of speech.