Elimination of flexible workpiece vibrations with a special damper, attached to workpiece by gluing, is considered. An unconventional approach for tuned mass damper application is proposed, based on damper tuning with respect to a certain spindle rotation frequency chosen for machining. Thanks to such tuning, the damper can operate successfully for workpiece with any frequency response function as long as the proper spindle rotation frequency is kept. Thus, a universal damper can be made using technique described, which can be applied for workpiece of any shape and frequency response with no preproduction preparations, providing an easy and fast way to avoid workpiece vibrations, which would be particularly helpful for small-lot production and model workshops. Theoretical investigations, experimental setup vibration testing and cutting tests were conducted. Workpiece vibrations reduction by 20 times was achieved, while device relative weight was just 2%. Finally, a real flexible part was successfully machined using damper prototype developed.