So I've been messing around with edges a bit, and have found that mewtwo does not grab the edge when doing any animation other than the fall animation. This includes his double jump animation. Because of this, it is easy to land on the stage when you were hoping for an edge which can be punished by an edgeguarding opponent.
There are a few ways to prevent this overshooting.
first and foremost, you can teleport and ledge snap. This is generally the best way, however on some stages the edges are rather funky, resulting in you SDing. You can also find the point at which mewtwos jump animation becomes its falling animation, although that can become fairly readable if used constantly. Finally, on stages slanted at about a 45 degree angle, you can wall jump into the edge to cancel his d-jump and land on the edge, which is fairly picky on location if you don't want to miss.
But thats just avoiding a missed edge. Now we can abuse that and mewtwos inability to cancel d-jump with an aerial.
If you double jump so that you will overshoot the edge and land on the stage, you have two mixup options for opponents on the stage (e.g. an edgeguarding gannondorf). if you overshoot you jump, then follow up with a bair (or uair if you're facing the stage), the attack will carry up through the stage and hit your opponent, allowing for a safer recovery (and even a kill at higher %'s). Generally go for bair because the range and damage are both better than uair unless you are facing the stage, in which case use uair. Use sparingly however, as an opponent can read, shield, and punish if you overuse this.