The cartoon opens with the credits in outer space and the camera pulls up to Earth, to a town somewhere in Oregon or Washington. Finally, right near deserted Highway 17, a flying saucer from outer space lands and surveys the surrounding area with a periscope. At the city dump nearby, Bugs Bunny comes back home, thinking he should move somewhere else, on account of the neighborhood "getting' terribly rundown."
Inside the spaceship, Yosemite Sam of Outer Space, dressed in a green gloveless spacesuit, sees Bugs on the television screen. Summoning Robot ZX29B to the bridge, he orders the robot to capture Bugs as part of their Earth mission. ZX29B trundles out of the spaceship to Bugs' hole and peeks down at him cleaning up after breakfast, making Bugs get the feeling he's being watched. ZX29B hides among some garbage cans when Bugs comes up from the hole with a pail of trash. Bugs thinks ZX29B is a new garbage can so he promptly opens his mouth like a lid and empties his trash into him. When Bugs leaves, ZX29B comes out coughing up the garbage.
Angered at "the stupidest robot [he's] got" for bungling his mission, Sam summons the Demolition Squad, a trio of red robots, and orders them to destroy Bugs. The Demolition Squad take fuselit bombs and go out into the dump. Seeing them coming, Bugs panics at being invaded and dives into the pipe leading to his bomb shelter. The robots dump their bombs down the pipe and head back to the ship. Escaping the shelter through a back way, an angered Bugs tosses a giant magnet down the pipe which sucks the "mechanized mobsters" into it. The bombs explode and blow the entire squad to smithereens, prompting a Medic Robot to appear and sweep up the mess.
Angered at the Demolition Squad for bungling their mission, Sam decides to go after Bugs himself and hops aboard an indestructible tank that he drives into the dump. When Sam scans the dump, he sees Bugs come up in a machine, which opens the tank hatch so he can drop a lit stick of dynamite into the tank. Sam tosses it out, but Bugs drops it back in and rivets the hatch shut. When Sam tries to hammer out the rivets, the dynamite explodes, sending Sam to drive his crippled tank back to the ship.
Bugs, at this time, decides to make his getaway by taking a handcar from the Flag Station. Just as he cranks away, Sam gives chase in the spaceship. The spaceship lowers a ladder and Sam goes down it, but he gets knocked off (and out) at a tunnel. The spaceship picks him up with a plunger and pulls him back into itself.
Sam catches up to Bugs via rocket pack and stops him at ray gun point. When Sam brags how Earth creatures can't maneuver very well, Bugs proves him wrong by spinning his ears like the blades on a helicopter and flies away. Sam shouts a catchphrase ("Yosemite Sam of Outer Space!") and tries to catch up by rocket pack, but misses when Bugs moves. When Bugs lands in a hole, Sam decides to wait so he can disintegrate Bugs the moment he comes out. While waiting, Bugs goes underground into an old tree stump behind Sam and secretly replaces his rocket pack with a lit stick of dynamite. Bugs flies out the stump and Sam, ready to chase after him, shouts his catchphrase just as the dynamite explodes and destroys his spacesuit ("Yosemite Sam of Outer - BANG! - Space?").
Back at the dump, Sam uses his Robot Ferret in his next attempt to catch Bugs. The Ferret descends Bugs' hole and encounters a Robot Rabbit built by Bugs out of old war surplus equipment. Sounding like Marvin The Martian, the Robot Ferret threatens the Robot Rabbit with a ray gun to go with him. The Robot Rabbit agrees, provided that the Robot Ferret doesn't press the button on his stomach. Nonchalantly, the Ferret ignores the command and presses the button, releasing a metal block which smashes him to pieces.
Angered at seeing the Robot Ferret in ruins, Sam decides that he's through fooling around. Bugs, meanwhile, builds another Robot Rabbit, sets a time bomb, puts it in the robot's stomach, and dresses it up like himself. Outside, Sam's spaceship draws out a huge ray gun and aims it down Bugs' hole, ready to blast Bugs, but Bugs, yelling out that he surrenders, sends out the decoy, which walks into the spaceship. Their mission "complete", Sam and the flying saucer take off and fly back to Sam's homeworld.
Later that night, Bugs turns on his war surplus radio and listens in as Sam presents the Robot Decoy to the planet's Potentate. The Potentate orders the Robot Rabbit decoy to come forward and when he orders the Robot to speak, its time bomb explodes in his presence. The dazed Potentate comments that Earth creatures always shoot off their mouths. Laughing at this, Bugs changes the channels, wondering if Amos and Andy is on yet.