Scratches on optical components induce laser damage and limit the increase in laser power. Magnetorheological finishing (MRF) is a highly deterministic optical manufacturing technology that can improve the surface roughness of optical components. Although MRF has exhibited significant potential for reducing subsurface damage and removing scratches, the principle and mechanism behind the scratch removal are not sufficiently understood. In this study, the theory of fluid mechanics is used to analyze the pressure, velocity, and particle trajectory distribution near a scratch. A physical model was developed for the differential removal of scratches at the bottom and surface of the optical components. The morphological evolution of the scratch was predicted during removal, and detailed experiments were performed to verify the effectiveness of the proposed model. The results indicate that scratches expand laterally rather than being completely removed. Furthermore, scratch removal efficiency is greater when the removal direction is perpendicular to the scratch rather than being parallel. This study offers an intrinsic perspective for a comprehensive understanding of the MRF technique used for scratch removal, which can be beneficial for removing scratches from aspherical optical systems.