Apparatus and method for sharpening a workpiece, such as a cutting tool. An abrasive disc is rotatable about a disc rotational axis and includes a plurality of spaced apart, radially disposed apertures extending therethrough from a first surface to an opposing second surface of the disc. The first surface is configured to facilitate sharpening of a workpiece by contacting engagement of the workpiece against an abrasive layer adjacent the first surface between adjacent first and second apertures of said plurality. The first surface further induces controlled axial displacement of the workpiece away from the disc as the second aperture approaches the workpiece during disc rotation. The first surface is preferably concave so as to extend into the disc between each adjacent pair of the apertures. Alternatively, the first surface is provided with different compressibilities to induce the controlled axial displacement of the workpiece.