He can deal damage with his shield because it's designed to work as a story element in a comic book. In terms of real physics, it makes no sense.
Newton's Third Law says that for every action there is an equal and opposite reaction. This is a pretty fundamental property of how masses interact with each other, and makes this concept fail.
The problem is that if we postulate some sort of material that absorbs the kinetic energy, thethat precludes the shield from imparting kinetic energy upon its target. This is because whatever is going on at the molecular or atomic level to do this absorbtion would also prevent the imparting of energy due to Newton's Third Law.
It's perfectly acceptable to me to postulate magical substances in comic books with physically impossible properties. However, there isn't a way to explain this one due to its asymmetric nature, unless the shield somehow "knows" which energy to absorb and which not to. I'm not aware of it being assigned any kind of consciousness, so that's out.