Random mutation is only one cause of genetic diversity
Shagging is the other one.
I'm no biologist (although I have just read wikipedia). My understanding is that our cells each contain a set of chromosome pairs, except for the sperm and egg cells, which have a set of unpaired chromosomes, ie half the number.
After a good ol' bit of bonking, mum & dad chromosomes all pair up to create a completely new set of chromosome pairs for the offspring. Additionally, the chromosomes themselves can swap bits of DNA with each other.
All rather tawdry, but the upshot is that sex can produce genetic traits that neither parent possess. Sexual species have vastly more genetic diversity than asexual species, and this greater genetic diversity leads to more rapid evolution. This is why all 'advanced' species are sexual.