In practical applications of laser cutting, the quality of the cutting surfaces is the critical factor. Recently, methods for studying the influence on quality of the main process variables have been developed, which seek to improve quality rather than explain the cutting mechanism. In the present study, a new method for circle and arc cutting is presented based on optical characteristic of a glass cone. In a laser cutting system, we use a glass cone to replace beam-focusing optics to direct the beam to the workpiece, and equipment for moving either the laser beam or the workpiece, or both, to obtain the circle or arc cutting pattern. Theoretical analysis and simulation studies of a glass cone show that the method solves an issue that the focal depth and focal spot can not be optimized, ensures the strict vertical cutting surface and the high cutting quality, and greatly reduces the workload caused by the motion of the beam or the workpiece.