To bite someone's head off 的意思是对某人严厉斥责、大发脾气，而且往往是在对方没有准备的情况下。

例句

I'm very sorry I lost my temper, I didn't mean to bite your head off.

Don't bite my head off, it wasn't my fault, I was just explaining the situation.

请注意

另一个短语 to bite your tongue 的意思是强忍住不说出、保持缄默的意思。

例句：

I had to bite my tongue to stop me from telling her what I really thought.