Place the Corian countertop, with the top of the counter facing downward, onto two sawhorses positioned on each end of the counter, giving you full access to the center of the surface.
Place the template for the sink onto the counter in the position that you’re installing the sink. Turn the template face side downward as well, so that the alignment of the sink is correct.
Outline the template on the rear of the counter with a thin marker. Remove the template from the surface of the counter.
Cover the drawn line with clear masking tape. The tape will allow you to cut through the Corian without causing any chips in the material from the teeth of the saw.
Drill a hole through one of the inside corners of the drawn template shape. Use a drill bit large enough to create a hole that can accommodate a jigsaw blade. Make certain the hole does not extend outside the drawn cutting line. Repeat the process for all four corners.
Push the jigsaw blade through the hole and align it with the cutting line. Use a high-tooth carbide blade for cutting through the Corian without chipping the material. Start the saw and then push the blade along the cutting line, using a slow but steady speed, with as little forward pressure as possible. Use the drilled hole in the corners to reposition the blade to create the next line in the cutout.
Place two suction cups onto the center of the template section after finishing the first three sides of the cutout. Have a helper hold the cups to support the section when making the final cut, to avoid the section snapping off before you can create a clean finish.
Pull up the cutout section and then remove the tape from the countertop surface. Smooth out the cut lines with a belt sander containing 50-grit sandpaper.