Yes. Article 2, Section 5 allows for expulsion upon the concurrence of 2/3 of the members. In the Senate that is either 66 or 67 depending on if the language is taken to mean 2/3 of all members(100) or 2/3 of the members voting(99 since presumably one doesn’t vote on one’s own expulsion resolution. No Senator has been expelled since the Civil War, so I would imagine that the finer points of the constitutional language would inevitably be litigated).
Unfortunately, that 2/3 vote will not be a tough nut to crack. The Democrats plus the technically Independents that are really Democrats hold 46 seats. The GOP establishment only needs 20/21 votes to join with the Democrats to make the 2/3 threshold. That’s around 40% of Republican Senators.
If McConnell wants Moore out, he almost certainly has the votes.
Then the voters of Alabama should send him back in the second special election, and the third, and the fourth, ad infinitum.
I am perfectly ok with a 99-seat Senate.
I'd prefer a zero-seat Senate.