Dr. Lawrence Angelo is a scientist working for Virtual Space Industries (VSI) in Project 5, a secret research facility that attempts to increase the intelligence of primates using psychotropic drugs and virtual reality (VR) training. Dr. Angelo is reluctant to use the research for military purposes, and after one of the chimps escapes and shoots a guard, Dr. Angelo is given a forced vacation. While taking notes on the need for experiment with a human subject, he discovers Jobe Smith (Jeff Fahey), a man with an intellectual disability who makes his living by doing odd jobs such as mowing the grass (hence the title of the movie). Angelo takes in Jobe, subjecting him to VR treatment. The first experiments quickly increase Jobes intelligence, but after an accident, Dr. Angelo stops the experiments. The Shop, a secret agency overseeing Project 5, reinserts the drugs responsible for Jobes violent behavior into the program and speeds up the treatment. As Jobe develops telekinetic powers, he starts to take revenge on those who abused him before he began the treatments, and plots to take over all of the computers in the world.

The SNES version continues the storyline after the point where it ends in the film. Jobe transfers his mind into VSIs computers, and from there is able to corrupt and destroy information systems all over the world, a course of action which is implied to bring about World War III. With society in complete meltdown, Dr. Angelo discovers that Jobe has been acting under the control of a person known as the Doomplayer, who is the head of The Shop, and poised to take over what remains of the world. With Jobe apparently having been erased now that he has served his purpose, Angelo sets off to put an end to The Shop once and for all.