No. There are no mechanisms to remove a sitting justice if they become debilitated. Many law review articles have been written to advocate for a constitutional amendment or other law to allow for a solution to the potential problem. Believe me, law professors gnash their teeth and tear at their breast when this subject comes up.

Since that's a short, boring answer, I'll discuss a few justices that had declining ability.

In the 1920s, Justice Pitney had a myriad of health problems, including a massive stroke. Chief Justice Taft wanted him to retire, but to his chagrin, Pitney refused. It wasn't just pride, though. The Judiciary Act of 1869 remedied an antebellum issue - Supreme Court justices were not provided a retirement with a pension. The Act allowed retirement, with full salary, if a justice reached the age of 70, served 10 years, and had good standing. Unfortunately, Pitney was 6 years too young. So, he wouldn't retire, but was far too unhealthy to handle his duties. Congress was forced to pass a special bill that made Pitney eligible for retirement benefits in order to nudge him to take the hint and get off the bench. At the end of 1922, the bill was passed and Pitney retired. He died two years later (Justice Holmes, in his late 80s and still going strong, quipped, "So they drop off, and I still remain like the Wandering Jew.")

Worse, Justice McKenna was eligible to retire, did not have the mental faculties to do the job, and refused to retire. In 1915 he suffered a stroke. In the following years, his mental decline was so noticeable that his fellow justices asked him to step down because the Court could not properly function. McKenna refused. Perhaps it was just pride. In any case, he absolutely could not do the job. He infamously wrote a simple opinion and managed to get the holding wrong. He went on like this until 1925, when the combined pressure of his colleagues and the reelection of President Coolidge finally persuaded McKenna to swallow his pride and retire - but he forced Taft to allow him to write a few more opinions! Interestingly, when confronted, he reportedly pointed out to the other Justices that they had no way of forcing him to retire.

So, there is no way to force a Supreme Court Justice to retire or otherwise remove them from the bench if they are physically or mentally unable to do their job. A combination of financial incentive and peer pressure has been used in the past, but a Justice like McKenna can be obstinate and really hurt the Court if they can't admit their ailments.

Just a note, OP: if you don't get answers here, you might try x-posting to /r/SCOTUS

The Constitution explicitly authorizes impeachment for 'high crimes and misdemeanors', which is a legal term of art dating to 1386, when it (and the associated concept) were first employed in England during the impeachment of the sitting Lord Chancellor, the 1st Earl of Suffolk.

Contrary to an intuitive reading of the phrase, 'high crimes and misdemeanors' has a very long history in American jurisprudence (and within the English legal tradition whence the concept was inherited) of encompassing essentially anything deemed problematic in relation to the accused holding public office, including, to quote Madison, "the incapacity, negligence or perfidy of the chief Magistrate." Although Madison did not mean 'magistrate' in quite the modern sense, the thrust of the remark is applicable to the case you have envisioned.

Hello all!

I have approved this post, but please remember to present all answers from a historical context.

This depends on the jurisdiction. For example, there are different rules for removing a Canadian Supreme Court Justice, an Indian Supreme Court Justice, or a Jamaican Supreme Court Justice. Without specifying which country, it is very difficult to say, or to give any historical examples of successful or unsuccessful attempts to remove a Supreme Court Justice.

However, you will find some good information in this primer from the International Institute for Democracy and Electoral Assistance: http://www.constitutionnet.org/vl/item/judicial-tenure-removal-immunity-and-accountability