An ultrasonic cutting system for stock material temporarily bonds the stock material to an anvil incorporated in a processing table and cuts the stock material at a low angle with an ultrasonic cutting tool. The ultrasonic cutting tool is mounted on a carriage assembly which traverses the width of the stock material. The ultrasonic cutting tool includes a cutting blade mechanically coupled thereto. The cutting blade resonates in response to ultrasonic energy travelling axially therealong. As the carriage assembly moves across the stock material, the stock material is first adhesively bonded or secured to the anvil by at least two rollers. The rollers are mounted on the carriage assembly at a position slightly ahead of the cutting blade. The rollers apply pressure in a downward direction on the stock material to temporarily bond the material to the anvil and to prevent it from moving or vibrating during the cutting process. As the carriage assembly moves across the stock material, the blade cuts through the stock material at a low angle, preferably at an angle of about 5.degree. to 10.degree. with respect to the horizontal. After the blade has cut through the stock material, a trailing shoe, slidably moving along a channel guide formed in the anvil, removes the stock material from its adhesive bond with the anvil and allows the cut portion of the stock material to be removed for further assembly and processing into a tire.