Disclosed is a numerical control apparatus for controlling a chopping operation of a tool used in a grinding machine and the like. A programmed instruction value calculation circuit (2) outputs an upper dead point instruction (Zu) and a lower dead point instruction (Zl), a correction value calculation circuit (3) calculates and outputs correction values (.DELTA.Zu, .DELTA.Zl), and a chopping instruction calculation circuit (4) outputs a chopping control output to a manual control circuit (6) based on these instructions and correction values to operate a servo motor. When an instruction value (Zi) is input from a manual pulse generator (5) to the chopping instruction calculation circuit (4), the chopping is effected while continuously changing the upper and lower dead points, thereby enabling an operator to easily adjust the upper and lower dead points.