He looks into the mirror, and peers into his own eyes. He sees what he saw, then he takes that saw and cuts the table into two halves. He puts the halves together to make a whole, and he uses that hole to get out.
he doesnt get out, the cube is solid, his only 2 posessions in life is the table and saw which is probably no where in sight, he will die in the cube unless action is taken by someone other than him.