A: It depends which Surprise you have, and when you play it.

If you have the promo No Free Lunch, found in the More Surprises pack, you can play it to prevent someone from utilizing Mystery Play (or any of its analogues, see below). The trick is, you’d have to play No Free Lunch when they declare they’re using Mystery Play, but before they reveal the card – you can’t wait to see whether it makes them win to declare you’re using No Free Lunch.

On the other hand the card that is drawn and played because of Mystery Play is affected by any of the “standard” Surprises. So if the winning card played because of Mystery Play was a Goal, then Canceled Plans would be able to prevent the win, since it cancels Goals. If the card played was a Keeper, you’d need to use the That’s Mine in order to stop the win.

Of course, you can’t cancel any of these if YOU are the one who is using Mystery Play.
See Can one ever use the “out-of-turn” function of a Surprise during one’s own turn? (spoiler alert: no)

*Note that you may be seeing this FAQ because your deck has a version of this card with a different name. There are so many analogues for Mystery Play that you should simply check the Fluxx Comparison Chart. Highlight the row for the Rule: Mystery Play, and scroll across to the deck you have to find the card this question refers to.