A method of processing a plate-shaped workpiece that includes on a face side thereof layered bodies containing metal which are formed in superposed relation to projected dicing lines includes the steps of holding a face side of the workpiece on a holding table, thereafter, applying a laser beam having a wavelength that is absorbable by the workpiece to a reverse side thereof along the projected dicing lines to form laser-processed grooves in the workpiece which terminate short of the layered bodies, and thereafter, cutting bottoms of the laser-processed grooves with a cutting blade to sever the workpiece together with the layered bodies along the projected dicing lines. The step of cutting bottoms of the laser-processed grooves includes the step of cutting bottoms of the laser-processed grooves while supplying a cutting fluid containing an organic acid and an oxidizing agent to the workpiece.