Machining simulation is a challenging task for numerical method due to inherent difficulty of modelling large-deformation processes. Smoothed particle hydrodynamics is known as an efficient and numerically robust way for solving large-deformation problems. The paper intends to address concerns in ultra-precision modelling of material at the micron scale. For this, planing experiments provide detailed data in terms of cutting energy for one crystal orientation at a time; however, a turning setup provides near continuous data for the entire range of cutting directions for a given zone axis. This study presents turning of single-crystal copper with the use of SPH. The model is implemented in a commercial software package ABAQUS/Explicit using a user-defined subroutine. The validated constitutive model is then used to gain insight into the effects of crystallographic anisotropy on the machining response of f.c.c. cubic metals to cutting.