A rotary working apparatus provided with a working unit and an actuator, wherein the working unit is provided with a unit frame and a cutter roll and anvil roll supported by the unit frame so as to be rotatable about mutually parallel axes of rotation, the anvil roll being further supported by the unit frame in a movable manner. The actuator is provided at the outside of the working unit and is provided with advanceable/retractable rods for making the anvil roll move to press the anvil roll against the cutter roll. A workpiece fed between the cutter roll and the anvil roll is worked by the rotating cutter roll and/or anvil roll.