The influence of damping and friction performance of grinding wheels on precision grinding was explored for the first time. GO hybrid PU-modified PF copolymers were prepared by in situ synthesis and adopted as a matrix for fabricating grinding wheels. FT-IR, DSC, TG, and mechanical property tests showed the optimal modification when PU content was 10 wt% and GO addition was 0.1 wt%. Damping properties were investigated by DMA, and tribological characteristics were measured by sliding friction and wear experiments. The worn surfaces and fracture morphologies of GO hybrid PU–PF copolymers were observed by SEM. Distribution of components on the worn surfaces was explored by Raman mapping and EDS. The research results revealed that the PU component tended to be dispersed around the edges of corundum abrasives acting as a buffer layer of abrasive particles, which could provide micro-damping characteristics for abrasives, making the grinding force more stable during precision machining and facilitating a smoother surface quality of the workpiece.