The mirror-universe Tuvok is a Vulcan who fights alongside the Terran rebels in the Badlands, appearing briefly in Through the Looking Glass as one of the rebel leader's trusted followers.
In the mirror universe Tuvok never served in Starfleet, which does not exist there. Instead he is one of the non-Terran members of the rebellion against the Klingon-Cardassian Alliance, based with Sisko's cell in the Badlands.
He appears in the Deep Space Nine episode Through the Looking Glass, played by Tim Russ in a crossover cameo made during Voyager's first season. He is present when the prime-universe Sisko is introduced to the rebels as their returned captain, and offers calm, logical counsel during the debate over what to do about Jennifer Sisko's sensor array.
The episode gives him little to do beyond this, and he is not seen again in later mirror-universe stories.