Let's look at how UU described his class ability. "Invites destruction through rage." Let's also look at how the trolls started falling apart after Gamzee had his spiritual upset and started going crazy. To me these things imply that Gamzee used his natural troll powers and his session-earned rage powers to pull at the threads of the other trolls' collective sanity. Making them kill each other in fits of anger, or make reckless and dangerous plans like going to join the side of the Sovereign Slayer.
Seems to me that Vriska really didn't want to kill Tavros, and only executed him on a whim because for some reason she felt like she had to.