Evolution doesn't quite work like that. It really affects populations, rather than individuals. Individuals within a population mutate and make new alleles all the time, but a single individual doesn't have to match their mutation with someone else's identical mutation to create a new species.
Allow me to use an example. Lets say you have a population of lizards living on both sides of a fault line. The lizards on the East side can freely pass to the West side, and vice versa, and all the lizards can mate with one another and produce healthy offspring. The lizards have stripes on their backs.
Now an earthquake occurs, making a deep rift in the ground at the fault line, which fills with water that the lizards can't cross. The lizards are then separated into two populations. Time passes, and gradually, each population changes. Mutations accumulate over each new generation, and both populations become different from what they once were. One group might end up composed of lizards with dotted lines on their backs, while the other might end up with zig zag lines. Eventually, a scientist comes along and tries to mate lizards from one side of the river with ones from the other, and it doesn't work. They can't produce fertile offspring with each other, since too many mutations accumulated between each population. Therefore, even though both groups are still lizards, the two populations, which were once all the same population, are now classified into two different species.
My point is that changes brought about by evolution do not generally work much on individuals. They work on whole populations.
The changes brought about in the lizard example might not have been caused by the lizard populations being separated. Even if the two groups had remained one, they still might have changed over time. If a lizard tried to mate with a time travelling lizard of a hundred thousand years prior, the two might not be able to produce offspring. This is because in any population, mutations, some of which remain in the population, and some of which are removed, change the phenotypes of the individuals. Mutations are generally unimportant - its just that sometimes a whole lot of them accumulate, and then a new species is formed.
I hope this clears things up a little.
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