Can a turtle breathe through their butts?

Answer 1

Yes indeed the can!
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http://www.straightdope.com/columns/011116.html
Of these the most remarkable, which some turtles share with dragonfly nymphs, sea cucumbers, and certain televangelists, is the ability to breathe through one's butt. You've heard the expression ‘Blow it out your after regions?’ It's no mere figure of speech. Many species have a pair of sacs (bursae) opening off the cloaca (combined digestive and urogenital chamber). These are heavily vascularized to facilitate the uptake of oxygen.

Answer 2

No.