In metal machining, the workmaterial undergoes severe thermomechanical loading, which has a consequence on the microstructure change at different zones in the machined workpiece (chip, tool tip zone, machined surface). In this paper, a multi-physics modelling in machining OFHC copper was proposed. The plastic flow stress of the workmaterial is described by the so-called Mechanical Threshold Stress (MTS) model. For comparison purpose the classical Johnson–Cook (JC) thermo-viscoplastic flow stress model is also introduced. In order to predict the microstructure change, precisely the grain size evolution in the workmaterial during machining, a physical-based Dislocation Density (DD) model was coupled with the MTS model in the framework of an Arbitrary Lagrangian Eulerian (ALE) Finite Elements (FE) approach. The ALE-FE model is developed for the orthogonal cutting process simulation in 2D case. Coupled MTS–DD material models were implemented in Abaqus/Explicit software via a user-material program. The first part of the multi-physics model is validated by comparison of predicted cutting force components with experimental ones and those predicted by the JC model. In the second part, the grain refinement during the cutting process is predicted, revealing zones where the microstructure is highly affected, particularly in the depth of the newly formed surface. This allows estimating the thickness of the effected subsurface by the cutting process.