A cutoff/milling device with a motor-driven cutoff/milling element, a work support surface or a guide surface, and a light projection device, the light projection device projecting a light beam onto a workpiece which is located on the work support surface or under the guide surface such that the light beam marks the cutting/milling position or cutting/milling path on the workpiece. The light projection device has a switch for activation of the light projection in response to mechanical vibration produced either by operating of the device or manual knocking on the cutoff/milling device.