The president of the United States has the power to nominate justices of the Supreme Court with the advice and consent of the Senate, in accordance with Article II, section 2 of the Constitution of the United States. Although the president has the power to nominate Supreme Court justices, he has no power to remove them; that power is reserved to Congress alone.
Article II of the U.S. Constitution defines the powers of the president. Section 2 of that article states, "He shall nominate, and by and with the advice and consent of the Senate, shall appoint ambassadors, other public ministers and consuls, judges of the Supreme Court, and all other officers of the United States, whose appointments are not herein otherwise provided for." Under the "advice and consent" portion of this clause, the nominee doesn't become a Supreme Court justice until confirmed by a majority vote of the Senate.
The Constitution states that justices "shall hold their offices during good behavior." Under this "good behavior" clause, Supreme Court justices serve life terms and can't be removed except for crimes or other serious misdeeds, as described by The Heritage Guide to the Constitution, a website sponsored by The Heritage Foundation.
For a justice to be removed from office, he or she must first be impeached by the House of Representatives, which has "the sole power of impeachment" as stated in Article I, section 2. If the House votes to impeach, a trial is then conducted in the Senate, according to the process described in Article I, section 3. If the Senate votes to convict by a two-thirds majority, the justice is removed from office.
No Supreme Court justice has ever been removed from office by impeachment, according to the Federal Judicial Center. Justice Samuel Chase was impeached in 1804, but was acquitted by the Senate and remained in office.