An exemplary brittle non-metallic workpiece (70) is made by the laser beam (31), a cutting surface (701 ) of the brittle non-metallic workpiece has no micro cracks. A method for making the brittle non-metallic workpiece includes: focusing a laser beam on the brittle non-metallic substrate to form an elliptic beam spot; driving the laser beam to move along a predetermined curved cutting path, making a center of a major axis of the elliptic beam spot intersecting along the predetermined curved cutting path and the major axis being tangent to the predetermined curved cutting path at the intersecting point; a coolant stream following the elliptic beam spot to move, thus producing a crack in the brittle non-metallic substrate corresponding to the predetermined curved cutting path; separating the brittle non-metallic substrate along the crack. A laser cutting device (40) for making the same is also provided.