In high-power laser systems, traditional small-tool polishing results in significant mid-spatial-frequency errors, which reduce the stability and reliability of such systems. In this study, we propose a polishing method that uses the compound swing trajectory (CST) based on a simple harmonic motion and demonstrate a polishing system that employs the CST of a multi-link mechanism. By analyzing the basic principle of small-tool polishing, we observe that the regular and orderly trajectories of traditional translational motion (TM) polishing are important causes of the mid-spatial-frequency errors. Further, we propose a function model based on a CST, study the basic polishing process, and perform the discretization calculation for such trajectories to improve the complexity of the trajectory of the removal function. We conduct a processing experiment by selecting appropriate process parameters and trajectories for the removal functions to compare the CST with the traditional TM. Subsequently, we measure the wavefronts using interferometers and observe that the interferometric fringe patterns obtained using the CST processing method are without burrs and smoother than those obtained using TM processing method. The power-spectral-density curve obtained using the CST processing method is lower than that obtained using the TM processing method in 50 mm×50 mm, displaying a better overall processing effect. These experimental results denote that a polishing system using the CST of a multi-link mechanism exhibits a significantly greater capability in suppressing mid-spatial-frequency errors when compared with the TM method.