Brown punch reciprocates continuously. Its motion source is not shown. It never contacts yellow slider carrying red upper cutter.
Two green rollers rotate continuously. Their motion source is not shown. They advance black rod thanks to friction.
The rod moves forward and pushes blue lever. This lever pushes the pink shim into the space between the punch and the yellow slider. The latter goes down to cut the rod.
Adjust position of orange slider to get desired length to be cut for the black rod.
The red stopper on the orange slider limits angular motion of the blue lever.
When the rod contacts the blue lever, it may stop for a while and the green rollers slip on it.
Disadvantage: the length to be cut can not be large because of the longitudinal bending of the rod.