Until I see otherwise, as far as I've seen, the Logia masters (those who've perfected their power, like Croc, Aokiji, and Enel, and not the people who just have the power, like Ace and Smoker) seem to be the most powerful in the series. They're practically gods of whatever element they use, and they can't be touched unless you posses their natural weakness. I guess that's why they're usually reserved for main villains, and big important characters. Logias just dominate.
I dunno if Mihawk can cut them, and I can't say he can unless it's stated (and "cuts the elements themselves" is too vague), so unless Oda says otherwise, I'll say he can't.