Demolition is a department in The Facility. They are responsible for destroying the tunnel leading in and out of the cabin area, preventing the victims from escaping.
During the Ritual, Dana Polk, Curt Vaughan, and Holden McCrea almost escape in their van due to a power rerouting glitch from "upstairs" that didn't give Demolition the orders to destroy the tunnel. To fix this, Gary Sitterson had to leave the control room and run to the Demoliton Department in order to fix the glitch himself and destroy the tunnel, preventing Dana, Curt and Holden from leaving.
In the Visual Companion, it shows that during the purge, a member the demolition team gets attacked by Zombies.
On the whiteboard, they bet on Mutants.