Mark with a grease pencil or marker the exact size and location of the area you intend to cut on the Corian surface.
Hang plastic sheets over doorways and air vents. Tape the plastic in place with masking tape to prevent the tiny Corian plastic and resin particles from spreading throughout the house.
Cover all furnishings and furniture with tarps. Tiny Corian particles stubbornly stick to many surfaces, making cleanup difficult without proper preparation.
Put on a micro-filtration particle mask and safety goggles.
Equip a drill with a standard carbide drill bit or a carbide spade bit, slightly larger than the jigsaw's blade. Drill two to three holes overlapping each other in the center of the section of Corian you intend to cut.
Install a specialized solid-surfacing material saw blade into a jigsaw.
Insert the jigsaw's blade into the drilled holes. Turn on the jigsaw and move it toward the guideline while creating a half round pattern that will line up with the edge of the cutting mark. Follow the drawn guideline with the jigsaw until the section of Corian is removable from the wall.