I played against a lot of Mewtwos at a smashfest last night. Here's what I think of him so far, as an opponent.
-Shadow Ball is mostly like any other charged projectile in terms of how we deal with it, as MagiusNecros said. I also want to note the insane recoil on it when Mewtwo uses it in the air. It can save him or it can screw him.
-WOW LOOK AT DAT DTILT! Mewtwo's tilt game is fast and well-ranged.
-Upthrow is still a kill throw, but not a particularly amazing one, especially against our heavy self.
-Awesome Fair by basically every measure
-Hard to edgeguard and gimp, due to the awesomeness of his teleport recovery.
-DUDE HE IS SUPER LIGHT! This is definitely his greatest weakness. He's really tall yet in the same weight class as Jigglypuff and G&W, it seems. Our Bair, Bowser Bomb, Fsmash, and Usmash will take him out really early, obviously.
Overall, he seems like a solid character so far, but his abysmal size-to-weight ratio is going to doom him to "mid tier at best" status, unless the next patch saves him.
EDIT: Upon retrospect, I should have posted this in the matchups thread or the social thread. I apologize for taking this off-topic, but I saw Mewtwo come up so I felt compelled.