Terrible idea. Any time a transporter duplicates somebody, one of them turns evil. (See the DS9 episode where Tom Riker pretends to be Will Riker and hijacks the Defiant, or the reason Harry Kim, who was replaced by his own duplicate early on in the series, never got a promotion).
So now you have to decide to kill Good Tuvix, or kill the other one, which will just give you Evil Tuvok and Evil Neelix.