The formal way of removing a supreme court justice from the bench:
Constitutional Language
Article 2, Section 4 of the Constitution states: "The president, vice president and all civil officers of the United States, shall be removed from office on impeachment for, and conviction of, treason, bribery, or other high crimes and misdemeanors." Because federal judges are considered civil officers, they are subject to this rule.
Article 3 mentions good behavior of judges, without defining it. According to the Congress.org website, produced by CQ-Roll Call Group, this is taken to mean that the reasons for impeachment of a federal judge aren't limited to criminal acts.
Impeachment Process
The impeachment process begins in the House of Representatives, with passage of articles of impeachment by a majority vote. The articles of impeachment state specific allegations of wrongdoing. The second step in the process is a trial in the U.S. Senate on the allegations. To convict someone who has been impeached, a two-thirds majority vote is required by the Senate. If convicted by the Senate, the accused is immediately removed from office.
Impeachment of Samuel Chase
The Federal Judicial Center lists federal judges who have been impeached by the U.S. House of Representatives. No Supreme Court justice has been convicted and removed, and only one has been impeached. The House impeached Justice Samuel Chase in 1804. The impeachment accused him of basing court decisions on political bias and misconduct. The Senate acquitted Chase in 1805 and he returned to duty.