is the advancement of macro evolution without hick up?

If an animal mates with another animal not of its exact species, the result will be a sterile creature (e.g. a horse mating with a donkey produces a sterile mule). If animals of a given species mate and produce an abnormal offspring (i.e. a mutant), it also is sterile. Therefore, how could the macro evolutionary process advance? How could a "mutant" (i.e. advances in form) reproduce? It would first have to be fertile itself. It would have to find a sexually compatible mate who was also fertile during its relatively miniscule life span on the overall evolutionary time scale. Thirdly, their offspring would also have to be fertile and be able to continue the advance. So if single celled animals formed in the primordial soup and they were asexual (not have either male or female characteristics, but reproducing by themselves, how would they advance to a hermaphroditic state (having both male and female sexual organs) and then to the higher orders of animals which almost always have distinct male and female reproductive organs? All in-between states are sterile.