In order to improve the cutting speed control performance of the ball screw sub-laser cutting platform, based on the principle of double power reaching law and fuzzy control a controller of gain fuzzy adaptive double power reaching law was designed. The Lagrangian dynamic model of the ball screw pair motion system was established by lumped parameter method for considering the various axial and torsional vibrations of ball screw pair. Meanwhile, the Stribeck friction model was introduced to estimate the friction that high-precision control systems were greatly affected by the high nonlinearity of friction. Due to the chattering of the traditional double power reaching law, the saturation function was introduced instead of the symbol function, which inhibited the chattering of control system to some extent. The fuzzy relationship between the laser cutting depth, velocity and gain was analyzed and established.The fixed gain was difficult to ensure the optimal dynamic control effect of the laser cutting, based on the laser cutting depth as the adaptive reference, the fuzzy controller based on the fuzzy rule table adaptively adjusted the control gain, which enhanced the robustness and adaptability of the system. Simulation and experimental results showed that it was not only solved the overshoot problem of the control system, but also improved the response speed and robustness of the system, effectively weakened the chattering of the system compared with the PI controller and the traditional double power reaching law controller. Meanwhile, the laser cutting laboratory platform was built. It was found that the best laser cutting depth range was 1/2～2/3 the thickness of the cell, and the best laser cutting speed was 200 m/s by the laser cutting experiment on the ball screw sub-laser cutting platform. On this basis, the PI controller, the traditional double power reaching law controller and the control method proposed in this paper were used for laser cutting. By comparing and analyzing the slit image of battery obtained by the metallographic microscope, it was showed that the slit of the cell obtained by the control method proposed in this paper is flat, which verifies the superiority of the control method proposed in the laser cutting speed control performance.