A cutting device for cutting flat material, such as sheet metal, is disclosed. The cutting device includes a knife shaft to which at least one circular knife can be fastened and a positing device. The positioning device is configured to move the at least one circular knife in a released state along a longitudinal axis of the knife shaft and to fix it in a predetermined position on the knife shaft in a reversible and force-transmitting manner, wherein the positioning device has at least one effector configured to actuate a clamping means of the at least one circular knife. The cutting device is further characterized in that to actuate the clamping means, the effector is movable along an axis of movement that is skewed with respect to the longitudinal axis of the knife shaft.