Systems and methods suitable for shaping and cutting materials. Such a system includes first and second carriage units that are independently operable to travel in a travel direction parallel to a longitudinal axis of a table supporting the material. The first and second carriage units have first and second arms, respectively. A cutting device coupled to the first arm forms a slit in the material, and a deburring device coupled to the second arm forcibly removes burrs from the slit. The deburring device is behind the cutting device relative to the travel direction and forcibly removes burrs in the travel direction toward a breakthrough point of the slit. The second carriage unit oscillates parallel to the travel direction so that the deburring device moves toward and away from the breakthrough point of the slit to remove burrs at the breakthrough point.