Prefered Stages

Town and City

Battlefield

Pokemon Stadium 2

Unfavored Stages

Lylat Cruise

Yoshi's Island

Yoshi's Story

Has to use his jump a lot and is a very weak character in the air just like little mac.
Mewtwo is pretty light and has a rather large hitbox.Use this to your advantage
Watch out for shadow ball as it can confirm into other hits as well as kill by itself
If you have a disjoint, keep in mind that if you use it against mewtwo upair/bair you will straight out win every time if timed properly. His tail is one massive hurtbox. Even without disjoints you can usually trade with those two moves
Trading IS GREAT against Mewtwo for midweights and heavyweights. Mewtwo is very light so he will reach kill percent before you if you are able to do smart trades with him.
Keep Mewtwo's specials in the back of your mind. Most of them are pretty situational, but you may still be caught off guard by down b or up b in neutral. Also keep in mind that side b reflects and depending on character Mewtwo can confirm it into Fair at 150+ and kill you.