The title question isn't entirely hypothetical under our Constitution, but in practice it may as well be. It's an idea most recently floated by Donald Trump during a rally in Wisconsin. Under Section 4 of the 25th Amendment, the Vice President, along with a majority of the principal officers of the executive branch may determine that the President is incapable of carrying out their duties and remove them from office. Trump pledged to support a Constitutional amendment that would expand that power to include the removal of the Vice President as well. This was clearly intended as a shot across the bow at Kamala Harris, supporting the idea that she should be removed from office for covering up President Joe Biden's cognitive infirmities from the press and the public. Of course, the likelihood of getting any Constitutional amendment to pass these days is essentially zero and this particular proposal would be fraught with problems of its own. (Politico)

Donald Trump on Saturday floated changing the 25th Amendment to allow Congress to impeach a vice president for covering up a president’s incapacity less than two months after President Joe Biden exited the 2024 contest amid concerns about his age and acuity.

“I will support modifying the 25th Amendment to make clear that if a vice president lies or engages in a conspiracy to cover up the incapacity of the president of the United States — if you do that with a cover-up of the president of the United States, it’s grounds for impeachment immediately and removal from office, because that’s what they did,” the former president said during a rally in Mosinee, Wisconsin.

The former president has repeatedly, and without evidence, accused Vice President Kamala Harris and Democrats more broadly of covering up the state of Biden’s health — particularly his mental fitness — after the president’s disastrous June debate performance that ultimately led to his exit from the race. Some Republicans in Congress had called for invoking the 25th Amendment, which provides a process to take power away from a sitting president, to remove Biden after the debate — the same rule Democrats attempted to wield against Trump after the Jan. 6, 2021, U.S. Capitol riot.

Let's all just pretend for a moment that it would be possible to ram through another Constitutional amendment in our lifetimes. (It wouldn't be, but we've still got some time to kill before the election.) You can't simply modify the 25th Amendment by adding the words "or Vice President" after "the President" in the first paragraph of Section 4. You would have a significant amount of rewriting to do because the entire basis of the 25th Amendment rides on the Vice President being the one to initiate the action, gather supporters in the Cabinet, and transmit their decision to the President pro tempore of the Senate and the Speaker of the House of Representatives. Unless the VP was actively attempting to remove himself or herself from office, they would be unlikely to do so. And if they were, they could simply resign and nobody could stop them.

Besides, if you really want to get rid of a Vice President that badly for valid reasons, there are other ways to do so. The Veep is subject to impeachment in the same way that the President, the Justices of the Supreme Court, and others are. Half a dozen Vice Presidents have had formal resolutions of impeachment inquiries filed against them, though none were ever removed from office. That list includes Dick Cheney and (drum roll...) Kamala Harris. Two Vice Presidents actually requested formal impeachment inquiries (John C. Calhoun and Spiro Agnew) but none were driven from office.

The entire idea of impeachment has been significantly cheapened in the modern era, particularly under Donald Trump. What was once seen as one of the most drastic steps that could possibly be taken, potentially signaling a constitutional crisis, has now been turned into a bit of partisan drama. Presidents are only supposed to be impeached upon proof being provided that they engaged in high crimes and misdemeanors. (We'll be arguing about the correct definition of misdemeanor in that context for as long as the nation survives.) If Congress was able to remove presidents for doing a bad job or lying about things, we wouldn't have a president last more than a few months for the foreseeable future.

In the end, the best and most reliable way to get rid of a Vice President (legally) is to defeat the president that he or she serves under in the next election. When you take the head off of the snake, the second head follows immediately behind. I honestly don't know what possessed Donald Trump to toss this particular red herring to the crowd. Perhaps it was simply another failure to remain on message and attack the policies of the Biden/Harris administration while pointing to the success achieved under his own. But I can assure you that this didn't move the ball forward at all. When Trump stays on message he has a winning hand to play. He should leave the tossing of red meat for the crowds to a qualified butcher.