Yeah, these are great pix and the likeness to a mantis is quite striking -- at least to human eyes. My guess is that this is not a case of mimicry, though.
The only reason that i can think of why it would mimic a mantis is for protection against predators, usually birds and reptiles.
Although this is a large insect --i think that the females get to be about 6"(15mm) long -- a mantis of similar size would hardly scare off a bird or lizard. Indeed we know that as a last resort, adult mantids put on an eidetic display by flashing their brightly colored wings which may cause a bird to be briefly startled and perceive them as larger than they really are. They do not warn off predators by extending their raptorial limbs. I would guess that the extended antennae simply make it look more twig like.
Still, these behavioral interpretations are often little more than guesses, and anthropomorphic ones at that. When you live alone with a dog, it is often hard to things to get mad about, but I tend to get pissed off by some of the anthropomorphic underpinnings in the interpretations of social altruism (sorry, friend Mike. I know that you are an E. O. Wison fan; I am, too!) , particularly something like the "stotting " of Thomson's gazelle.
And for anyone who has somehow missed seeing footage of the mimic octopus on Animal Planet, here you go:
http://www.youtube.com/watch?v=6iby1HFR-4g&feature=fvst