When Fox flies in with a SHFFL Neutral air or down air, a DA Dash/Pivot grab really screws with the Fox's attempts to cross up or space in front of you allowing you to grab him in the air where he can't shine, or you mess up his L-cancel timing and get more shield grabs for your tech chases and combos.
You don't try to challenge Fox in air superiority, you challenge his limited aerial mobility and priority from being underneath and you challenge the Fox's ability to space and L-cancel aerials. You want the Fox to play you like he would play his Marth/Sheik friends and not like he should play Mewtwo.
If you get upsmashed from teleporting away from Fox, you're just doing it wrong. You have to Teleport CANCEL, meaning you teleport while slightly in the air and only receive normal landing lag instead of the full teleport lag. Also, you don't teleport away to any place where you can easily be read or punished.Make slight movements, small wavedashes outside of his neutral air range, space your tilts, and do what you HAVE to do against just about every other character.
If you're getting read and punished for being evasive, then you're most likely being out played. Mewtwo can stall almost indefinitely against every character. Fox is one of the hardest to stall against, but if you force Fox to attack you, you get more openings. If the Fox forces you to attack, you have a higher risk of getting grabbed > up throw > up air.
If you know he's going to shine you after your aerials, then don't go for the grab after the aerials and move away. You have to be able to tell when the Fox misses L-cancels to shield grab those.
Fox's Neutral air, if you distort his spacing and move into him, or force him to overextend should just about always give you grab opportunities since it shouldn't be as safe as a frame perfect drill shine. Move into him with your shield or move away from him with proper spacing.