Spray or smear caulk softener on the caulk surrounding your laminate backsplash. Let the caulk softener soak for the amount of time recommended by the manufacturer -- typically one to two hours.
Lift the edge of the softened caulk with a putty knife and peel the caulk strip away from the backsplash. Scrape away any remaining pieces of caulk with the putty knife.
Examine the edges of your laminate backsplash for any screws or nails holding it in place. Remove them with a screwdriver or hammer claw.
Set the saw to a cutting depth of 1/2 inch so you can cut through the backsplash and the substrate its attached to without damaging the drywall behind it.
Put on protective goggles. Turn on the circular saw and slowly cut through the backsplash.
Put on protective gloves. Grasp the backsplash by the cut and pull each piece away from the wall. Discard the old backsplash.