[crypt2k]

If a mutation occurs in an individual to produce a new species, what organism does that individual mate with to
perpetuate the species?

[spoiler2]

It's not just the genetic mutation, but suitability with the ambient life conditions in place, that cause the individual to progress.

If a particular genetic mutation makes the individual less able to adapt to the prevailing conditions, it dies.

However, if the surviving individual then mates with another individual who has survived the same conditions due to their own mutation, the resulting offspring would then be stronger in that particular direction, whether it's longer legs, more fur, or any other of the limitless variables that can occur.

[Junior]

If a mutation occurs in an individual to produce a new species, what organism does that individual mate with to perpetuate the species?

Speciation does not occur in an individual, but within a population. The population gradually changes over thousands of generations. If, for some reason, a population is split into two or more separate populations (a mountain range bisects its range, for example), the separate populations will gradually diverge from one another giving rise to two separate species.