The utility model relates to a modularized cutter with digital control in the polar coordinates, which is characterized in that it comprises of a linear motion device, a pole shaft device, a pole routine device, a cutting head device and a controlling display device. On the linear motion device, a moving platform is arranged, which connects with the pole shaft device. A pole routine device, which rotates around the pole shaft device, connects with the pole shaft device through the connection component on the device. On the pole routine device, the controlling display device is arranged, also is the cutting head device that moves along the shaft direction of the pole routine device. The utility model is designed with the concept of modularization. It can choose the cutter bar composition device and alternate cutter bar cutting function according to different occasions; each component device of it is designed in polar coordinates and is suitable most to cut the circular, round annular and fan-shaped work pieces. With the same slide way, the cutting range of the polar coordinates cutter bar is 2 times as many as those of the right angle coordinate cutter bar. And the procession range can further expand by replacing the devices concerned.