When I first read that I thought, "Sure, why not?" Now that I think more about it, manti have some pretty ferocious spikes on their front legs. This is what they use to capture prey. I don't know what kind of fight a mantis would put up while being eaten, but if your turtle caught one of those suckers in the eye...
To be safe, I'd refrain. Plus, manti are such a great thing to have around the garden. There are so many other food options, it seems almost a waste. But, if you're really inclined you could always pre-kill the mantis.
You know, when I was a kid my buddies always said that if you killed a stick bug, preying mantis, or chopped down a dogwood tree you could be thrown in jail for 20 years. I don't know if feeding your turtle is worth that kind of incarceration.