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Microstructural deformation at the grain level has an inherent impact on the achievable ultimate machining accuracy of polycrystalline materials. In the present work, numerical simulations and experiments of diamond cutting of polycrystalline copper are carried out to investigate the formation of surface step at grain boundaries on machined surface. Single crystal diamond cutting tool with straight cutting edge is chosen for experiments to mimic the tool geometry utilized in 2D crystal plasticity finite element simulations. Moreover, the same crystallography configuration of bi-crystal Cu is employed between experiments and simulations. Formation mechanisms of surface steps at grain boundaries are revealed by finite element simulations and corresponding experimental validation, as well as cross-sectional transmission electron microscope characterization. Finally, finite element simulations of orthogonal cutting of bi-crystal Cu are carried out to examine effects of both extrinsic cutting edge radius of diamond cutting tool and intrinsic misorientation angle of grain boundary on the propensity of grain boundary surface step formation. The present work provides theoretical guidelines on the strategy of suppressing grain boundary surface step formation for achieving superior surface finish of polycrystalline materials by diamond cutting.