The invention provides a metal cutting numerical control system based wire cutting machine control method and device and a computer storage medium. The method includes the following steps: determiningone of a first machining trajectory located at a first surface of a workpiece and a second machining trajectory located at a second surface as an arc trajectory; cutting the first machining trajectory and the second machining trajectory to obtain a first group of continuous straight line segments corresponding to the first machining trajectory with a predetermined number and a second group of continuous straight line segments corresponding to the second machining trajectory with a predetermined number; interpolating the straight line segments of the same arrangement position in the first group of continuous straight line segments and the second group of continuous straight line segments into the machining directions of the first machining trajectory and the second machining trajectory atthe same time in order; and controlling wire electrodes of a wire cutting machine to machine the workpiece. The method of the invention enables a metal cutting numerical control system to be directlyused for the machining of wire cutting special-shaped surfaces, which improves the generality of equipment.