The Vice President is an elected official just like the President. He doesn’t work for the President and he’s not subordinate, he just has almost no power.
The only way to remove a VP is death or impeachment. I suppose the President could induce death, but that’s not really firing per se.
He could literally throw him under a bus and not suffer any legal consequences. It's probably 50/50 whether or not senate Republican would vote to impeach him after that.