Nixon fired spiro agnew. I mean. Technically Agnew “resigned” what with the accusations of corruption, tax evasion, whatnot. Point is, the president can demand the resignation of the VP. And in normal times, the VP would comply.VP is an elected office. They can only be impeached - not fired.
In today’s climate it would not be surprising if the president asked the VP to resign, and the VP refuses. So that would be fun.