How does one get kicked off the U.S. Supreme Court?

Impeachment/Removal is a purely political question. A President, federal judge (including a Supreme Court Justice), or other federal official can be impeached whenever and for whatever reason the House of Representatives thinks it proper to vote to impeach, and can be convicted and removed from office whenever and for whatever reason the Senate thinks it proper to vote to remove after impeachment.

That being said, after the 1804 impeachment of Justice Samuel Chase, the strong American political consensus is that you do not impeach judges for their judicial views and decisions. This, however, is just a working consensus that can change any time Congress thinks it should change. For instance, if a Supreme Court Justice were to start publicly and unrepentantly espousing racist views, there is a strong possibility that Congress could find that worthy of impeachment and removal. On the other hand, if it comes out that one of the Justices called somebody the N-word in 1982, it would never happen.

If there were a case where a Justice were mentally or physically disabled, it was clear that he or she would be in such a condition for the rest of his or her life, and he or she were unable or unwilling to resign, and that this would persist for several years (i.e. a Justice had a stroke or were in an accident where he or she couldn’t communicate to resign, not a situation like Chief Justice Rehnquist where terminal cancer took his life several months after he became unable to work), there is a chance that Congress could “more in sorrow than in anger” vote to impeach and remove (while likely immediately thereafter reinstating his or her pension and medical benefits).

But in the special cases of judges, who are required to be neutral and impartial, and treat all litigants and witnesses equally, I think there is a good argument that racism and anti-semitism are more than just a moral failing; they amount to an inability to carry out one’s constitutional duty to judge fairly and impartially: a breach of the duty of good behaviour required by the Constitution.

Exactly - the house and senate are not bound by precedent, just by good judgement. (Aha, the problem becomes clearer). In many cases, as Billdo points out, the decision is probably more political than legal or concerned with “justice” (as a concept). Thus, for example, the Democrats were not about to vote to remove Clinton as president, despite blatant lying, since it would damage their (house, senate, and white) chances in 2000 even more than it eventually did. Republicans took advantage of this to advance the impeachment secure in the knowledge they were not giving the next president - Gore - a squeaky clean head start, or they would have voted against impeachment too.

In the case of a blatantly offensive racist judge, the house and senate would have to weight damage to the reputation of the court, whether they wanted to vote for or against a racist individual and what that did to their re-election chances; and not least, what creating a vacancy on the court at the time does to the current and future options for filling the vacancy, since judge selection is highly political. Sotomayor had to deal with a sexist/racist allegation, Thomas with a sexist accusation - neither rose to the level of excluding the candidate.

I don’t think we can take that much from the Chase case, that bias can never be the basis for removal. That’s particularly the case since the Senate is a political body, not a court, and is not bound by precedent.

Normally, things like an allegation of bias by a judge are dealt with through the appeals process, not via impeachment and removal.

However, what if the bias is so clear and so serious that a litigant cannot reasonably expect justice from that judge? Does it not then breach the duty of good behaviour?

Suppose a sitting judge said: “Chief Justice Taney was right. The Founding Fathers never intended that darkies could be citizens of the United States. The 14th Amendment and the Civil Rights Act were horrible mistakes. The Constitution and the laws shouldn’t give them the same rights as white people.”

I would think that type of statement might make the Congress think about impeachment. As Billdo says, ultimately impeachment and trial are political in nature. The Congress gets to define what is “good behaviour” in the context of a federal judge.

But as a matter of practice, it seems to be followed. Look at the judges who have been removed from the bench since 1804. All of them have been for a specific act: joining the Confederacy, taking bribes, tax evasion, perjury, molesting interns.

For all the talk about impeaching judges after decisions like Dred Scott or Brown or Roe or the 2000 election or Kelo, there’s never been any attempt to actually follow through. No judge has ever been impeached just for making decisions people didn’t like.

The Master did address this, just a couple years ago: There goes the judge: How do we get rid of whacked-out judges? - The Straight Dope

Since when has being out of their mind stopped any Justice from doing their job?

I think you have to find an example of a federal judge who did make racist statements (or whatever) before that becomes good evidence.