Well that was fun to read. Always like learning about Japanese though I don't have time to learn it on my own, just random things I pick up. So I'm guessing the first character, mu, is sort of like a modifier. Since it means "no" or "zero", when paired the second character assumes the meaning of "limit" or "boundary" or something along those lines. But by itself "kiri" means bird.
I was really hoping MUKIRI meant "Infinite Bird" or something like that though.