Complex sentence: The Puppet Master uses radioactive clay to make puppets of people that he can then control, attaching them to strings and moving them as puppets; presumably he has some sort of psionic ability that enables him to do this.
Split into simpler sentences: The Puppet Master uses radioactive clay to make puppets in the likenesses of real people, whom he can then control by attaching the clay puppets to strings and moving them about. Presumably he has some sort of psionic ability that enables him to do this.