The simulation of machining of soft metals at the 100 microns-few mm length-scale requires capturing complex flow physics induced by the high ductility and polycrystalline aggregate nature of these metals. This work presents a remeshing and mesh-to-mesh transfer approach that can successfully simulate complex flows including highly sinuous flow with surface folding in polycrystalline aggregate cutting. The meshing scheme is both graded and adaptive, with the ability to automatically refine regions such as self-contacts. Notably, the presence of microstructure makes these simulations far more complex than their homogeneous counterparts, with several additional constraints on the remeshing algorithm. The approach is general, with no limitations on rake angle, grain-size, or friction coefficient, and does not use an artificial, predefined separation layer. The scheme accurately tracks individual grains and allows grain splitting in a manner consistent with imaging experiments. The plastic strain field, cutting-force evolution, and deformed grain shape from several annealed-copper cutting simulations are presented, representing a range of rake angles and friction coefficients as high as 0.5. The simulations accurately capture the thick chips, high cutting force, and highly undulating streaklines of flow that characterize sinuous flow, as well as the experimental observation that the sinuous flow is suppressed on using a high rake-angle for the cutting. Moreover, in grains that are split between the chip and residual surface, we can accurately capture the extreme grain stretching that is observed prior to splitting in imaging experiments. Remeshing also provides a way to accurately capture the residual surface plastic strains and strain gradients. The latter are particularly steep, with the strain falling from a value greater than 10 to 2 within a distance of 30 microns. The use of remeshing has numerous advantages over a predefined separation layer, including the fact that one can parametrically explore the effect of variables like the extent of yield stress inhomogeneity on the flow pattern with no limitations. Interestingly, the technique allows us to find the actual line of material separation in such cutting processes: As opposed to a horizontal line, this is typically an undulating curve with a deviation of about 0.06 of the undeformed chip thickness on either side of the horizontal. This fraction increases with the extent of sinuous flow. A simple, pseudograin model with spatial inhomogeneity in flow stress is used to represent the microstructure in the present work, but the present scheme can easily be used with more complex microstructural models as well.