Robotic cutting is a challenging contact-rich manipulation task where the robot must simultaneously negotiate unknown object mechanics, large contact forces, and precise motion requirements. We introduce a new active virtual-model control scheme that enables knife rocking motion for robot manipulators, without pre-planned trajectories or precise information of the environment. Motion is generated and controlled through switching virtual coupling with virtual mechanisms, given by virtual springs, dampers, and masses arranged in a suitable way. Through analysis and experiments, we demonstrate that the controlled robot behavior settles into a periodic motion. Experiments with a Franka manipulator demonstrate robust cuts with five different vegetables, and sub-millimeter slice accuracy from 1 mm to 6 mm at nearly one cut per second. The same controller survives changes in knife shape and cutting board height, and adaptation to a different humanoid manipulator, demonstrating robustness and platform independence.