Mutation occurs when the genetic structure is changed in the parent, or during transmission. Mutants are not created by being dropped in vats of glowing goo, or by heing bitten by a radioactive spider. The average accidental mutant is destroyed within the womb, as the body determines it will not survive and terminates it automatically. In real life, this is what happens to a vast majority of 'mutants'.
But it's no fun to role play an biologically aborted fetus, and CyberSphere is a post-apocalyptic role playing game. This means that mutants are part of the background, as the freaks left by generations after the bomb.
If you're looking to play a mutant like Wolverine or The Tick, think again. Expect to play something more like Ratlord, or a failed Tom Savini experiment. Take the average human, and put the genes in a blender. One eye, three eyes, scales on their arms, faster blood clotting, color blindness, and brittle bones for example. A mish-mosh of recessive traits and traits not often seen within nature, forming something from the Enquirer's photo bank.
In the world of CyberSphere, the mutants born after the blast were shunned and rejected by society. Facing death at the hands of many groups, such as Humans First!, mutants in most major cities fled. Some chose to live in the sewers, with the scum and rats. Some lived near the blasted damage part of the city, their genes already warped, most of them sterile anyway. Few obtained proper education, and few would be accept at any standard societal function.
In New Carthage, the vast majority of mutants that survived persecution from the moment of birth fled to Old City. Those less able to live above ground live in the sewers, forming a struggling society of beggars and scavengers. By staying in numbers, they manage to avoid being slaughtered outright by Humans First! and other organizations.