Since the cutter is not moving with the web, it must stop when being cut. Nothing you do with the pull rolls will change that. You can either stop the rollers during the cut, or let the material buckle between the rollers and the cutter. If you allow buckling, then the measured length between cuts may change.
Many thin webs do not have enough stiffness to be pushed between the rollers and the cutter, particularly if the web has already buckled. That is why multiple drive belts are often used above and below the web to carry it to the cutter. They cause the web to be wavy (corrugated) in the cross plane, which makes the web stiff in the machine direction so that the web can be pushed into the cutter. The cutter will flatten the web as it cuts it.
There is only light friction between the drive belts and the web (no pinch) so the material can stop during the cut, without stopping the belts.