For all of our scars, for all of our freedoms, we will fight our mutual enemy, to sever the chains that binds us.
—Scar Chain's yell
The reason Scar Chain is fighting towards the destruction of Deadman Wonderland, is for the sake of "freedom".
Scar Chain (自由の鎖 (スカーチェイン), Sukā Chein; Japanese for "Chains of Freedom", sometimes called Skull Chain) were a group of Deadmen that opposed the prison and planned to leak the truth to the rest of the world. They believe in each individual's own personal definition of freedom. They were lead by the Deadman Owl (real name Nagi Kengamine). His second-in-command is Karako Koshio, also known as Game Fowl, who secretly loves Owl and fights for his sake.
They set up an operation to escape DW, but in the end only a few members of Scar Chain escape.