Yeah, I get it. You don't want to go
As you open the door, Wizzrobe meets the gaze of the Medusa and is turned to stone!
any more than you want to go
As you open the door, Wizzrobe dies!
So, first off:
0) Monster moves are how GM moves happen.
Like, look at the lich. One of its moves is to cast a perfected spell of death or destruction. And sure, that's a way to deal damage, but when done on the ceiling it's a way to separate them, if it slowly tears a path of destruction toward Clericsdottir it puts someone in a spot, and if you tell Wizzrobe how the runes all flash by so fast but their shapes are so familiar, that offers an opportunity that fits a class's abilities.
So when one of the cool things you've written down that a monster can do is "transfix with a stone gaze" or "transform interlopers to swine", okay, you'll probably want to start out with moves that foreshadow future badness or put people in a spot, but ultimately no matter how much you go
The rune of pigification traces itself out beneath your feet! You taste bacon. What are you doing?
You catch a glimmer of the medusa's emerald eyes and your legs start to stiffen. What are you doing?
people are going to roll 5, 4, 2, and 3 and you're going to have to commit to it. So in that case, and for that case, because you really shouldn't be dropping instadeath or its second cousin on your PCs without doing some prep:
1) Seek a way out!
Okay, so once you're stone you can't just will your way out of it. That makes sense. So, how can you get out of it? Wizard's got Ritual. Cleric's got a deity to petition. You can just say what you like as a GM there.
And of course, with an effect as powerful and noteworthy as this, there's got to be some Lore that anyone could Spout about it, and the ways to break out. Maybe Bard (Arcane Art) and Paladin (Lay on Hands) could work then, or at least give you a shot at clawing yourself back from the brink.
But not everything has to be true forever.
2) Consider making it "just for long enough".
Rather than being permanently charmed to switch allegiance, or plunged into the forever-sleep, or completely paralyzed, an effect can have a decent impact even if it only works for a single inopportune moment.
The crocodile pit looms in front of you, gaping and... somehow inviting? Yeah. Inviting. You should just give Sir Justice a shove, Leafwillow, and all that armor would just weigh him down. These are totally your thoughts and not at all related to the glowing eyes of the stone crocodile statue opposite the pit.
Mark XP if you do this thing you completely legitimately just thought of, or Defy Danger to think of something else.
Granted, mental effects seem a lot more temporary, but even a medusa's gaze or polymorph spell that needs to be refreshed once a day can turn a total party statueing into something else.
3) Consider making it "build over time".
Just 6 on that Hack and Slash, Fightgar? Well, alright then, here's what happens. You go in for the shot, figuring that's just an ornamental sword and she's got no kind of grip on it. It turns out it's one of those form-follows-function sorts of ornamental with a good sturdy edge, and she hasn't got so much no grip as every grip? She moves like a snake, which makes more sense now that I say it out loud.
Anyhow, three increasingly off-balance parries later, you finally manage to go where her guard isn't and strike a glancing blow. Give me damage minus 1d6? And in the rush of combat, you've completely forgotten this isn't an enemy you can lock eyes with.
Everything in you recoils backward and it seems to take forever, but you do scatter free, though your breathing is labored and your chest feels like it's make of lead, or something similarly dense and inorganic. If you could, write down on a clean space of your character sheet: "Fightgar = Statue", and then draw four circles next to that. And then fill in two of them.
Shanksworth, you saw something of how she moves and it's pretty clear those eyes could find their way pretty much anywhere. So while Fightgar's staggering backward, what are you doing?
Yes, it's completely legitimate to give people, in addition to their stock of Hit Points, a stock of Not Being A Statue Points or Not Yet A Pig Points. That way you can "deal damage" to it and get palpably closer without having to try and make people feel more threatened through description alone.