I actually like fighting Marths. I just love the MU.
Nguz is right. When Marth is above you, you should be wrecking him. Mewtwo is a beast when his opponent is above him because of U-air's & Utilt's crazy range. And Marth is *** above his opponent so of course you always want to capitalize there. Just watch out for the dair from Marth, he might throw it out if he's getting juggled pretty bad.
In the neutral Mewtwo should be throwing shadow balls, hovering around until you can effectively make an approach or you can just zone and make Marth come to you. The second option is probably the best one. Teleporting around Marth and using shadow ball out of teleport makes it even harder for him to close in on you if he's trying to stop your zoning. If he does eventually break your zoning jabs & dtilts are pretty much your fastest options to hit him before he hits you, HC Fair/Uair are both pretty fast as well. And watch for bad spacing from the Marth a shield grab can net you a quick 30-50% if you capitalize effectively.
When Marth is offstage, that is where you want to get aggressive. You should be trying to gimp a Marth everytime he goes offstage, with your great edgeguard and his fairly predictable recovery you have a complete advantage over him in this area. One bair/dair can easily take a stock from a Marth offstage, you will just have to watch for his recovery mixups, of which he doesn't have many. If you are dominating the ledge vs a recovering Marth you are probably going to win the match. Imo this is the most important aspect of the MU for Mewtwo.
You also can space Marth out. I wouldn't rely on it more than shadow balling him but it's possible and effective when done correctly. Your Ftilt outranges everything from him besides maybe his Fsmash. And your Fsmash has more range than his does. Ftilt can be used simply to knock Marth back a bit while you go back to zoning. I wouldn't try to challenge his CC game too often because his dtilt will beat yours if he CCs.
In my experience:
-Shadow Ball Zoning
-Closing Edgeguards
-Juggling
-Spacing
If you are performing well in those areas you are winning the match.
I like fighting Marths too, although (at least in Melee), I think it's admittedly a bad matchup for Mewtwo.
I don't know exactly just how much more effective Mewtwo's shadowball zoning is in PM over Melee, but I would usually recommend against it. While it is a way to slip in some damage at Marth at if he's far enough, a good Marth with good footing will try to crunch the space between you and him where perhaps he's not in a full out offensive, but he's just properly spaced so that he can punish you if you attempt an uncharged shadowball. I find it more than being a zoning strategy from Mewtwo, it's more of a counter to Marth's own zoning, expecting you to come at them. Making Marth get into that range is probably what you meant when you said "making Marth come to you" I guess.
Also, I noticed that while Marth's are away from you trying to persuade you into coming at them, you can charge your shadowball all the way through, since the moment you start charging, they're expecting you to release it and they get ready to counter it or avoid it, which allows you to just continue charging. I think the idea of "well that dude just stood there and charged his projectile all the way through" seems rather unlikely to some of us, since I fall to that against Samus players too.
Anyway, when Marth is at that range, I think it's best to begin playing the spacing game. I guess Marth players like to think that they can create this pressuring and safe flurry of attacks, but it turns out that Marth has many holes in his pressure. You want to bait Marth into moving while spacing until you get the right time to punish. Marth's like to use retreating fair, for example, since this puts pressure unto the opponent, puts Marth in a constant position where Mewtwo's dtilt approach is not a threat, and puts Marth into a relatively safe landing position. However, if the first fair is shielded or outspaced, Mewtwo can wavedash into Marth and go for a shieldgrab, a crouch-canceled dtilt, or even just u-tilt out of the wavedash for a juggle since being above the opponent can be so bad. I don't know how much more hitbox he has in his uair OoS, but I wouldn't be surprised if it's really any easy counter too like MK0 says. If you have a fully charged shadowball (or an almost fully charged shadowball, which is more prone to make the Marth forget that you have one), you can also usually have the Marth eat it if they try these types of strategies.
Getting Marth on a platform above you is also usually favorable since you can come in with a nair, which tends to shieldstab for land them on another platform. Making it hard for Marth to get out of unfavorable juggle positions. A stage with platforms may also favor you if you're good at shield-dropping and can find timings to punish Marths attacks from under the stage although a good Marth may try baiting these or waiting out on your shield for shieldstabs, which is another reason that PM needs light-shielding direly.
What I find to be the biggest match-breaker in Marth's favor is his grab though. All is fine until Marth just starts dashing in an grabbing you out of your dreams for victory, although it's hard for him to get a kill on a Mewtwo that can properly DI, but then you have to rely heavily on your wits to return to the neutral game. Mewtwo's new spot-dodge probably makes that less of an issue.