If it makes you feel better, I have yet to win a tourney match as M2. Nope, every single game I used him has gone to last stock last hit. Needless to say I get too ancy and choke.
Anyways, my matchup list for M2 that I ballparked.
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I don't think Mewtwo really has a matchup better than 60:40. His frailty means upsets are always a factor for the opponent, and his neutral, good as it is isn't oppressive enough to make his weight a non-factor.
Samus may be disadvantaged by having her staple projectiles reflected, but she has faster attacks, can harass with her zair and use her homing missiles to bait reactions, plus she has effective combos.
Duck Hunt also isn't that simple, since his projectiles all eat shadow balls of any kind, and no Duck Hunt is just going to sit back and chuck them while you reflect. His issues with killing also aren't quite as severe with Mewtwo.
On the flip side, Kirby is outspaced too hard for it to be his advantage, but he can use his small size to open opportunities for good damage others would miss out on and can outbox up close so it's not too bad for him either. Jigglypuff... not so much. She has Rest, and... that's it, really. Mewtwo pretty much stomps her anywhere else as long as he's not TOO reckless. Her not being susceptible to combos is cold comfort when you unquestionably die earlier than anyone else, not to mention Mewtwo's good damage per hit circumvents the floatiness somewhat anyhow.
Bayonetta is too early to really say, but her neutral isn't too difficult for Mewtwo to handle (just watch for dive kicks), plus he has the boons of being able to avoid all of her gimping tools (including Witch Time), and not having to risk the aforementioned counter for the kill. The only real question at this point is exactly HOW effective her combos are on Mewtwo.
Yoshi isn't as safe as he looks, and when it comes down to it isn't great at sealing the stock either. He has to mix-up a lot to get his hits in, since a lot of what he does can be countered, even stuff like his fair and nair.
Finally, while Sheik does truly outneutral Mewtwo, having an answer for most everything Mewtwo does, he has the tricks necessary to stay in the game, namely avoiding gimps and being able to score lethal damage and blows without hard commitments.