Place the Corian counter top with attached back-splash in the desired installation location, pushing it flush with the wall, or walls, and any other items. You may need an assistant to help move the counter top.
Identify the exact place where you want to cut the Corian piece. Place a straight edge on top of the counter top at that location, and use a pencil to draw a line where you want to cut. Reposition the straight edge, and extend the line onto the back-splash.
Move the Corian counter top outdoors or to another well-ventilated location, such as a garage. Position it on top of two sawhorses so the pencil line is easily accessible.
Put on safety glasses and a dust mask. Install a carbide-tipped blade in a saber saw or reciprocating saw, and plug the saw's power cord into a nearby electrical outlet.
Squeeze the saw's trigger to start the blade vibration. Move the saw blade slowly and steadily along the counter top's pencil line until it reaches the attached back-splash.
Reposition the saw blade over the top of the pencil line on the back-splash. Cut through the top of the back-splash until the saw blade intersects with the cut you made in the counter top. The counter top should separate into two pieces. Turn off the saw.
Carry the piece of counter top that you want to use to its installation location, and check whether or not it fits in its space. Cut more from the counter top and back-splash if necessary.