Fox definitely kills Mewtwo early on FD. However, when M2 gets a grab he gets automatic combo damage or a backthrow to set up for edgeguard damage. Fox generally only gets bursts of significant damage, but lacks the ability to flow from one sequence of combos and chases to another. His uthrow uair doesn't set up for air chasing very well due to Mewtwo's unique ability to teleport down and his decent air maneuverability. He's pretty much limited to drill shine -> tech chase and uthrow uair for 20-25% max.
I agree that it's hard for Mewtwo to gimp Fox (aside from occasionally dsmashing an illusion -> ledgedrop bair). If Fox up-b's high to recover onto the stage or a platform, he's virtually unpunishable. I think if Mewtwo covers every option, he can do it. But Melee's just such a fast game and Fox has a lot of mix-ups.
Fully charged shadow balls, of course, are useful when Fox is offstage. But I think Mewtwo has some gimping potential with an uncharged shadow ball. Accurately targeting Fox as he charges his up-b with even an uncharged SB causes Fox to drop lower, reducing his options and also giving you time to go offstage with bairs in some circumstances.
I mean, obviously Fox is a really hard match-up for Mewtwo, especially if it's a professional Fox player we're talking about, but if the Mewtwo is also very good (which is rare; Taj and Iori would be good examples), Mewtwo can handle him.
If Fox dash dance camps, you can shut it down to some degree with shadow ball spam. If he approaches with nairs or dash attacks predictably, you can CC -> dtilt. If he uses dairs to counteract this, you merely dash dance grab or pivot grab him. Laser camping is problematic, but most people will get antsy after a couple blasts in tournament even and will opt to bring the fight to you more often than not.
I completely disagree. Fox can very easily keep Mewtwo on the ropes from landing any aerial or grab. Mewtwo's only saving grace is that he falls down from shine and has a very long tech, but because of how far he goes it is VERY easy to follow and Mewtwo almost always has to tech away.
Backthrow is percentage dependent and grab dependent. Fox can land grabs on Mewtwo easier than the other way around. I don't know what Fox players you're playing. Yes I can obliterate average Fox players, but good Fox players have no problem landing their up throw up air and even if it isn't a straight combo, it is an easy link to a second or third series of up airs to take you from 0-60% and you still haven't touched the ground yet. Mewtwo is very weak when Fox is below him and good Fox players can easily turn that 60% you just took into a quick stock by 50/50ing your landing.
Fox is a fast faller. Sure, Mewtwo can teleport down, but he isn't invincible in initial frames. Mewtwo is floaty, so depending on where he teleports down Fox can be right there grabbing or putting on pressure. Mewtwo's recovery is good... as long as he has a second jump, but Mewtwo is so large that Fox can always take ledge and pressure the teleport recovery from almost ANY situation. The only way to survive is to always cancel the teleport. From certain situations... it can be tricky or impossible.
Drill shine isn't the only problem. Fox can chain neutral airs on Mewtwo very easily as well, and those link into up smashes.
It is impossible for Mewtwo to cover every option of recovery against Fox most of the time. Shadow balls only work if they try to start recovering from above the ledge. If you land it, great, he MIGHT drop too low to sweet-spot, but it doesn't have that much stun. If you hit Fox with standing shadow ball to stop a forward B or up B, then they can still just forward B again and get ledge. The only way to stop it is if you are already at the ledge and you're doing shadow ball to down smash, but they can just drop and up B from that position and going high unless they're at ~140% will prevent any kind of counter KO even if you call it. The best thing you can do is grab and back throw them again at that point, then they can recover from an even higher position.
Shadow ball doesn't stop Fox's dash dance at all. Fox just lasers as you throw it, shields and lasers, then resumes dash dancing. Fox has the superior projectile. If you use it to try and approach, Fox can just go to a higher platform. On FD Fox can just jab it, reflect it, neutral air through it, dash away range it, side step, or do the first thing I said. You can't CC Fox's neutral air with a down tilt, YOU MIGHT be able to grab him if he timed it incorrectly, but drill shine is flawless, neutral air shine is a threat, and if they're in the motion of shining, they'll CC your down tilt and punish you without effort.
Average Fox players might get antsy, good Fox players might get antsy, but they won't make any technical errors. They can bring the fight to Mewtwo and they still have way more cards than Mewtwo.
I don't want to sound condescending or anything, but this Mewtwo delusion has to stop. Yes, a good Mewtwo can beat a good Fox, but you have to understand that on paper, this is an impossible match-up. Sure, Mewtwo has a monster combo on Fox with up throw that pales in comparison to Fox's, but landing that is not only difficult, but it isn't necessarily guaranteed because of DI.
Mewtwo is a fun character, I'm trying to make him competitive at a high level, and I've succeeded. Is he legitimately viable at a high level? I'd have to say yes and no. Mewtwo works best against people that haven't played against him. I still do well against Forward, Axe, and Wobbles. They know a lot of my tricks, but I also know them a little bit. This game isn't so shallow that my Mewtwo can't beat a good Fox, but it is still unbalanced enough to where Mewtwo doesn't do well against Fox on 3/6 neutrals and EVERY counter pick stage.
I will continue to advance Mewtwo's metagame and find a way to overcome these huge disadvantages, but I urge every Mewtwo player and fan to not dismiss these weaknesses. You can try to use theorysmash all you want, but I've taken my Mewtwo around this country and I've seen a lot. You have to keep in mind when you're trying to create scenarios that you're playing chess without a rook and bishop, you can only cover so many options.
Thank you for your input, I'm taking everything into consideration.