A high-precision, numerically controlled, diamond cutting machine has been developed for fabrication of asymmetrical aspheric mirrors, such as toroidal mirrors used in SOR optics. In this machine, a work-piece is securely fixed to a machine base, and its side face is cut by a flying single-point diamond tool. A tool spindle is laid on an X-Y slide, and its position is numerically controlled by using a laser interferometer. It is possible to fabricate a cylindrical surface by having the spindle-axis rotate slightly about an axis perpendicular to the X-Y slide. Furthermore, while the spindle is rotating, cutting-depth can be dynamically controlled by utilizing a piezo-actuator fixed to the diamond tool. The cutting-depth control is synchronized to the current rotation angle of the spindle, and cutting-depth data are numerically programmed as function of X-Y slide position. A suitable combination of these programmable figure parameters allows fabrication of asymmetrical aspheric mirrors. In order to achieve high figure accuracy, accurate straight motion is required with the X-Y slide. Therefore, straightness error compensation control is adopted, which incorporates a ZERODURE straightedge of 1m length and three optical-fiber gap sensors. The machine accepts a work-piece with maximum dimensions of 600mm length and 100mm width. A figure accuracy of 0.1 μm and surface roughness of 0.03μmRmax have been achieved.