Some mutations would be part of a species gene pool and they would all be born with these common traits eg Mutant Cat Men with Heightened Int, Heightened Senses, Natural Attack I (Claw) etc (Fairly realistic). I guess this could be covered by an origin ?
Things that are basically a species, like the cat men, should get a specific talent. Things that are actual mutations can be handled by making a new, custom talent, picking a talent with the
Diverse ability, or taking the Test Subject specialty (although you might want to rename it).
However, at any time (birth or otherwise) mutagenic agents eg Nanite Clouds could add random good or bad mutatations to any character. (Bit of wild and wahoo GW stuff). So one of the Cat Men above could also have a natural carapace on his back and a vulnerablity to mental control. Only he would have these traits. So I guess would be a Feat ?
Make a special group, call it Mutation Feats and go from there. If you're using a system for mutations like d20 Apocolypse make it a small group where the first gives access and some points to buy them and the rest make things 'better'. If you're using a system like Darwin's World or Gamma World d20, just use the rules presented there, the randomness factor is enough of a balance. Ideally, you'd want to replace the rules and specifics of the mutations with NPC qualities, powers from Archer conversion, or even 'normal' character options.