Efficient movement - You want to be able to act quickly after everything. Especially offstage, on the edge, after attacks (especially throws and d-tilt), and off of WD. Offstage is very important because Mewtwo has a lot of gimping power and can cover a lot of high recoveries with the bair super jump that conventional characters would struggle with. Being able to grab the edge with teleport opens up a lot of option coverage that he otherwise misses out on (and gives him a lot more time to wait onstage or whatever, which is good - not having to commit early is very good).
DJCs - Self-explanatory. They're mostly combo tools but they have other random uses (DJC nair OOS is kind of cool, uair is good under a platform, and I'm sure there's more stuff). You should get comfortable hitting them at varying heights. A lot of people who pick up DJC characters for funsies only can do them at ground level but you need to be comfortable doing them at multiple heights because sometimes combos and situations just go that way.
Attack Angles - Because, quite honestly, Mewtwo can't ever win exchanges with priority against good characters. He has to constantly aim where there isn't a hitbox, when their move is done, etc. So get used to doing everything with some kind of weird angle involved that allows your move to slip under theirs or whatever. This is difficult to practice on your own but you should at least try to get a feel for it.