Trollwut derives from the terms troll (an individual on the internet that angers others for entertainment), lol (short for "laugh out loud"), and wut (term used to denote extreme confusion). The term "trollwut" is used in the same style as "lolwut", but is typically directed at 1) someone who is attempting to troll someone and failing or 2) between friends who tend to use sarcasm as a basis of humor.
1) Jim: Ur t3h n00bz nd u shld g0 hom3 2 mmmy and cri!!11!
2) Jim: I totally scored with your mom and sister last night.
A statement made after someone has committed an act of such great stupidity and foolishness that the questioner is too gob-smacked to fully comprehend why someone would do such a thing. Akin to the terms wat, wut, and what, but used to infer complete and utter shock/anger.
(After Jim shot Tim's character in a video game for no apparent reason)