Krang contacted General Traag in Dimension X and had him send the Minimizer to Earth through the portal. The minimizer exited the Technodrome and flew up to the Earth's surface to begin its assault by shrinking all army bases that might cause trouble for the Technodrome.
Krang and Shredder use remote-controls to pilot the minimizer from a control room inside the Technodrome. It is sufficiently user-friendly that Shredder declares that even Bebop and Rocksteady are able to control it.
The minimizer is capable of shrinking anything it fires its rays on. Its purpose is to reduce resistance by shrinking military bases. It then fires a tractor beam at the shrunken object, pulling it inside a hold in the Minimizer. The Minimizer is also capable of firing destructive energy bursts; it fired at April O'Neil when she was following it in the news van.
The Turtles hijacked the Minimizer by jumping onto it, and used it to shrink the Technodrome. The minimizer crashed and was never recovered by Krang; Donatello apparently cannibalized its parts in order to create a ray that would restore the shrunken bases to normal, although this event was never shown. However, since Krang designed the minimizer, he could easily restore the shrunken Technodrome.
The design of the Minimizer appears to be inspired by the Martian war machines depicted in the 1953 film The War of the Worlds. It's green-colored energy bursts further the connection.