An ultrasonic cutter cuts edge chamfers of plate-shaped workpieces using a cutter head which forms an axis of rotation and a blade which extends from the cutter head and forms a cutting wedge, terminating in a straight cutting edge, between flank and contact faces determined by the wedge angle. In order to create advantageous structural conditions, the axis of rotation extending on the blade side of the flank face is at a distance from the flank face which is equal to or greater than the distance of the center of mass of the blade from the flank face and the cutting edge, extending in the direction of the axis of rotation, extends at a distance from the axis of rotation which corresponds at most to the blade thickness.