From the Super Mario Wiki
Roughly the size of a small moon, Koop Star was built for domination of the Mushroom Universe. It was the fastest known spacecraft to have ever been built, and was capable of reaching speeds of up to Warp 10. Known machines that were a part of Koop Star include a tractor beam, the Birdo Ray, and the Intergalactic InSinkErator.
In "Star Koopa", Darth Koopa and Mouser used Koop Star to pursue the Flying Pizza, which they captured with Koop Star's tractor beam. When Darth Koopa succeeded in freezing Mario, Luigi, Princess Toadstool and Toad, he brought them aboard Koop Star, where he failed to coerce Princess Toadstool into ordering the Mushroom Space Colonists to surrender their planet to him.
Knowing that Princess Toadstool wouldn't change her mind, Darth Koopa ordered Mouser to activate the Birdo Ray, and to toss the four heroes into the Intergalactic InSinkErator, where he expected them to be killed. However, due to some quick thinking by Mario and Luigi, their group jammed the Intergalactic InSinkErator's blades with utensils, causing them all to get packed into a single Garbage Pod while still alive. The Garbage Pod was then ejected out of Koop Star, and transported Mario's group to the Mushroom Colonists' Planet.
At the Mushroom Colony, Obi-Wan Toadi told Mario's group that the only way to save the planet was to penetrate Koop Star in a Mushroom Starfighter, so that one could disable the Birdo Ray. Once they were equiped with Mushroom Starfighters, Mario, Luigi, Princess Toadstool and Toad flew back to Koop Star, were they were attacked by Stormtroopas in their own starfighters. Mario's group managed to fight off the Stormtroopas, allowing Mario to fly into a canyon-sized groove along the surface of Koop Star. After some close calls with a few Stormtroopas and protuding walls, Mario entered Koop Star through a small hole, and blew up the foundation of Koop Star with a Bob-omb. As a chain reaction, Koop Star as a whole blew up as Mario flew off, while Darth Koopa and Mouser escaped into deep space on a Space Raft.