The tenth amendment does indeed provide for all rights not stated in the Constitution to be the property of the States and the people. However, in the removal of a Senator from the Senate, the Constitution gives that power to the Senate, so the tenth amendment does not give that power to the States or the people.
Article I Section 5
Each House shall be the judge of the elections, returns and qualifications of its own members, and a majority of each shall constitute a quorum to do business; but a smaller number may adjourn from day to day, and may be authorized to compel the attendance of absent members, in such manner, and under such penalties as each House may provide.
Each House may determine the rules of its proceedings, punish its members for disorderly behavior, and, with the concurrence of two thirds, expel a member.
Right. It amazes me how many supposed constitutionalists are willing to ignore the plain language of the Constitution when it suits them.
The Constitution says a senator serves a six-year term. Nothing about “six years unless he becomes really unpopular with the voters at home.” In fact, the whole point of having a Senate was originally to have one house be farther removed from popular control.