Silicon carbide (SiC) has been widely used in optical components due to its excellent physical and electronic properties. However, it is very difficult to process the SiC owing to hardness and chemical stability. The robot bonnet polishing method was proposed to solve the problems existing in current polishing SiC optical elements methods, which have a low material removal rate and are expensive. First, according to Preston equation, Hertz contact theory and velocity analysis, the removal function model was established, the bonnet polishing head device was designed and put through simulation analysis. Next, aiming at the problem that the workpiece surface is prone to ripple errors during the traditional periodic polishing path trajectory processing, a pseudo-random polishing path based on the traveling salesman problem (TSP) is proposed. The path has the characteristics of multi-direction, high randomness, flatness and continuity, and compared with the raster path and random disturbance path, it is verified that the improved TSP polishing path has the ability to suppress the spatial intermediate frequency error. Then, single-point and multi-point polishing experiments are implemented to verify the accuracy and stability of the removal function. Finally, the application verification polishing processing of the SiC optical element is implemented by rough and fine polishing. The experimental results show that the bonnet polishing method and the improved TSP polishing path can effectively achieve the polishing of SiC optical elements and better suppress the intermediate frequency error of the optical processing surface. After three cycles of rough polishing and four cycles of fine polishing, the surface profile convergence rate is 72.3% and 50.8%, respectively, and the convergence rate is faster and the machining accuracy is higher.