http://www.google.com/patents/US9017322
As far as I can tell, the idea is to use evanescent coupling to transfer light into hair follicles. There's no free space laser beam, just an optical fiber that you drag across your face. They also claim that chromophores (color bearing molecules) in hair can be severed at relatively low powers with a mixture of several specific frequencies of light.
So, what this product needs in order to work is a fiber that's durable enough to survive being dragged across skin while having very little cladding so as to allow evanescent coupling. That could be very hard to do, so the heads on these laser razors may wear out after a few shaves just like a metal razor. Second, they need to pack a high power multi-wavelength laser source and the power reserve to run it into a very tiny handle. Again, this is probably going to be pretty tricky.
There's nothing here that looks outright impossible to me. Just very, very tricky.