In a web cutter where a blade is used to cut a continuous paper web into sheets, a tractor is used to move the web past the blade for cutting. The tractor operates in a start-and-stop cycle so that the web is temporarily stopped to allow the blade to lower and shear the web. The tractor accelerates in the next cycle to move another length of paper downstream from the blade. A high-speed cutter requires high acceleration of the tractor. This acceleration force causes the web to whip up uncontrollably, causing the web to break or wrinkle. To reduce the web breakage, a moving mechanism positioned upstream from the tractor and operate a second motion cycle is used to move the web toward the tractor such that a loop of paper is formed upstream of the tractor, thereby reducing the whipping action of the web.