(coexisting on another dimensional plane)
Tuvok was a Vulcan member of the Terran Rebellion against the Klingon-Cardassian Alliance in the mirror universe. Typical of his species, he was notably less impulsive than other members of the Rebellion such as Julian Bashir and Rom and preferred a logical approach to combating the Alliance. Nevertheless, he was as surprised as anyone by the apparent return of the presumed-dead Benjamin Sisko. (DS9: "Through the Looking Glass")
The script mentions that Tuvok was the leader of a different faction from Bashir and that he was "a coldly logical soldier". (Star Trek: Deep Space Nine Companion - A Series Guide and Script Library)
The mirror Tuvok is the only mirror universe counterpart of a Star Trek: Voyager regular character to ever appear on screen. He is also the only mirror universe counterpart of a regular character to ever appear outside of their counterpart's "home" series. He reappeared in the novella The Mirror-Scaled Serpent, along with the counterparts of other USS Voyager crew members as well as in the short stories "Bitter Fruit" and "Empathy" contained in the anthology Shards and Shadows and the novel Rise Like Lions. As with his primary universe counterpart, he is married to T'Pel and has three sons, including Sek, and a daughter named Asil.
According to The Mirror-Scaled Serpent, Tuvok was the slave of the mirror universe version of T'Kar for many years. This was an in-joke based on the fact that both characters were played by Tim Russ.