We already have a process. Impeachment. Congress can’t just vote a President out as that would violate the Coequal branches of Govt. This is a stunt and going literally nowhere.
Technically, they can. A clause (Section 4) in the 25th states that the vice president and the majority of the cabinet can call upon Congress to remove the president because he is somehow unable to fulfill his duties. This section was written in case the President is comatose or otherwise incapacitated and cannot, via Section 3, voluntarily cede over power.
This amendment was not written as a way to create a coup. This is what Pelosi is trying to do. There is a phrase in there "or of any such body as Congress may,
by law, provide". That is the real purpose of this bill... to throw up a dog whistle to Democratic voters to be sure to vote for those Democratic candidates in those close senatorial races - they can get Trump out if he wins by doing it this way.
You have to look at the timing of this bill. The NC senate race is all but lost and Tillis will be re-elected. There are a handful of close Senatorial races still in play. Dems need to flip the Senate badly and are pulling out all the stops. This bill has no chance of even making it to the floor, doubtful even out of committee. It is simply political theatre.