Apparatus and method for sharpening a cutting tool, such as but not limited to a kitchen knife. In accordance with some embodiments, a flexible abrasive disk is adapted for rotation about a central axis at a selected rotational velocity. Centrifugal forces imparted to the disk during rotation urge the disk to a neutral position in which an outer peripheral portion of the disk is extended toward a selected plane. A housing adjacent the flexible disk has a guide slot with a guide surface at a selected bevel angle with respect to the selected plane. The guide surface is adapted to facilitate presentation of a cutting tool in contacting engagement against the disk. The cutting tool is presented at the selected bevel angle to induce curvilinear displacement of the flexible disk during sharpening of a cutting edge that extends along a side of the cutting tool.