Kryptonians can handle magic just fine, they simply don't have any unusual resistance to it. An "exploding arm" spell would work just as well against Clark as it would against Dinah in a way that tying C4 to his arm would not. However, it's still an exploding arm spell. If you have a magic pot that's designed to always have water in it, and you hit Clark over the head with it, it's going to break and he's not going to even notice. Mere "magic" doesn't hurt him, only specifically offensive magic does. This applies even to weapons - Mjolnir is the perpetual example DC uses, in that Mjolnir wouldn't hit Clark any harder than it would hit anyone else, because the enchantment on it is about unbreakability and worthiness, not "deal extra damage in addition to the normal force of impact."
Minerva's claws are magic, as far as we know, only inasmuch as she wouldn't have them without magic. Whether they deal damage above and beyond what they're physically capable of is an issue canon is silent on.