From the Congressional Research Service:
The authority of the United States Senate (as well as of the House) to establish the rules for its own proceedings, to “punish” its Members for misconduct, and to expel a Member by a vote of two-thirds of Members present and voting, is provided in the Constitution at Article I, Section 5, clause 2. This express grant of authority for the Senate to expel a Senator is, on its face, unlimited — save for the requirement of a two-thirds majority. In the context of what the Supreme Court has characterized as, in effect, an “unbridled discretion” of the body, expulsions in the Senate, as well as the House, have historically been reserved for cases of the most serious misconduct: disloyalty to the government or abuses of one’s official position. The Senate has actually expelled only 15 Members — 14 of those during the Civil War period for disloyalty to the Union (one of these expulsions was subsequently revoked by the Senate), and the other Senator during the late 1700s for disloyal conduct. The House of Representatives has expelled only five Members in its history, three during the Civil War period, one in 1980, and another in 2002, after convictions for bribery and corruption offenses related to official congressional duties. In the Senate, as well as in the House, however, other Members for whom expulsion was recommended have resigned from office prior to official, formal action by the institution....