If I have damage on me, and I use Mewtwo's "damage change" on the opposing Suicune, does the damage still get removed off of me? (even though it won't go on Suicune because of it's ability)
Yes. The damage counters on Mewtwo-EX would be removed and then "disappear," while the counters on Suicune don't move as they cannot be affected by Damage Change.