Use a razor blade to carefully cut through the caulk around the countertop, including caulk underneath the front lip of the counter. Gently pry the countertop up from the cabinets below and carefully slide off.
Lay the granite countertop face-down on a large work table. Slip pieces of scrap lumber under the edges of the countertop to raise it up slightly and prevent cutting the table. Clamp the granite and scrap lumber securely to the table. If the countertop extends past the edges of the table, support it with more scrap lumber.
Carefully measure and mark the places to cut the granite to fit the desired project. Clamp a metal straight edge to the granite to act as a guide for the saw.
Wearing safety glasses, ear protection and a dust mask, carefully cut the granite using a circular saw fitted with a masonry blade. Make several passes with the saw, starting with the blade set for a shallow cut and lowering the blade slightly each time.
With the cut complete, unclamp the granite and wipe away any dust or debris from the cutting.