I actually have a lot of experience in this matchup and play about 15 games with a Mewtwo main last week. He is probably one of the best Mewtwo's, his tag is Prof, and he has beaten Lambchops (multiple times) and other top South Florida players in tournament.
Anyway, my opinion after playing him is that the matchup is slightly in his favor but maybe even. The fact of the matter is it is really hard for either characters to approach. Mewtwo just never really approaches in any matchup in general but he does have the shadowball. Shadowball is a decent projectile but in most of the top tier matchups he is playing against characters that are fast enough to get through them and never really give him an opportunity to set up potential pressure situations using shadowball. Unfortunately, DK doesn't really have a great way through them so you have to jump over or use platforms. Shadowballs are good against DK but it isn't really what tips the matchup in M2's favor (although he can throw the charged shadowball at our terrible horizontal recovery and bop us).
M2 has really good juggle combos on DK and it is absolutely imperative that you DI everything away in order to get out of it. If you get caught in the air whether it be from an upthrow or utilt, he can juggle you with 1-2 upairs and then backair another 2-3 times across the stage. It is actually pretty easy to string backairs against Mewtwo and sweetspot up B on his shield is really good since its somewhat easy to shield poke his shield. As for cargo combos, you can always hit him with an aerial and you can do cargo uthrow to uair at high percents (all the way up to at least 110) for a kill so we have reliable kill power on him, but uair juggling him is not as easy because teleport instantly gets him out (I felt like I usually got 2 but rarely 3 uairs in a row). Another thing that mewtwos like to do is teleport from the ledge mixed in with stalls and a few other things. The best we can do to punish that is one of our less laggy aerials (so not fair unless you get the read) before he buffers roll. If you have the punch that is another story. Both characters have a lot of trouble ledge guarding each other as long as you know how to recover with up b. He will try to downsmash but you should be able to get through it with proper sweetspotting unless he stands very close to the ledge with really good timing. But dair will kill us because DK.
In summary, he is hard to approach and ledgeguard. His punish game on us is surprisingly good and his range on his tilts can compete with our normally good range advantage. That being said, we have reliable kill set ups on him and our backair can string together. Suprise fairs, mid % punches, and good dair setups can take stocks from him early where as he doesn't have much in the way of killing us before 100. With good reads, I would actually say its probably 50-50, we just can't play "safe" or he will just shadowball camp.
