Mutants are deformed creatures, usually humanoids. A mutant is different to a Cyborg in that a cyborg has mechanical parts and deformities, whereas a mutant has biological growths and deformities. Insect Mutant is also the only mutant to appear in more than one game.
Whilst mutants have been spotted before 2052, the mutants still seem to have originated from the U-Genix company, successor to The Brotherhood of Ultra Science and owned by Jacob Crow, still crazed by his search for immortality. U-Genix mutants are extremely similar to the TimeSplitters that Jacob Crow eventually creates in 2243. The reason mutants may have ended up before 2052 could be because Crow needed a place to hide his hideous experiments, and the past would have been the perfect hiding place.
Mutants are not to be confused with the undead. Even though they may walk and act similar to zombies, mutants are different in that decapitating them will kill them (unlike some zombies which may continue to attack) or that they do not necessarily have to be decapitated, unlike story mode zombies.