Which is correct, "buck naked" or "butt naked"?

They're both "correct", and they both mean "totally naked" (although "butt naked" can mean "bare buttocks").

The etymology of "Buck naked" is apparently lost to time, I'm afraid. To add to the list of suggestions already made: From the phrase "as naked as a buck deer" (which apparently is similar to the phrase "naked as a jay-bird").

"Buck naked" is the older term:

Both phrases currently mean the same thing but one could argue for "butt naked" meaning someone with a naked butt.

EDIT: "Older" in the context I used it above appears to be either incorrect or extremely misleading. Other, conflicting, sources are popping up so it is good to take this graph with a grain of salt. It also doesn't surprise me that other variations exist (e.g. bare-butt naked).

I think it is safe to call this one a tie: Either variation is perfectly acceptable and anyone claiming that one is "more" correct is just shoehorning their experiences onto the English language.