Rayman rescues Grand Minimus along with 3 other teensies who open up the Hall of Doors which allows him to travel around the universe.
The Grand Minimus appears in his throne room, telling Rayman it is not safe to keep Globox there. He opens the portal to the Teensie Highway and tells Rayman to take Globox to the Teensie Doctor, Otto Psi.
Rayman frees him at the start of the game after he was imprisoned by the Rabbids.
Grand Minimus was intended to be one of the main members of Rayman's crew, as he appears in all story-related cutscenes, as they save the Glade of Dreams from the nightmares in Origins, but was replaced by Green Teensy, and was placed as a unlockable skin, by saving 70 Electoons.
In Rayman Legends, he is now a true member of Rayman's crew and one of the default Teensy skins.