During the machining of carbon nanotube (CNT)-polymer composites, the interface plays a critical role in the load transfer between polymer and CNT. Therefore, the interface for these composites has to be explicitly considered in the microstructure-level finite element (FE) machining model, so as to better understand their machinability and the interfacial failure mechanisms. In this study, a microstructure-level FE machining model for CNT-polymer composites has been developed by considering the interface as the third phase, in addition to the polymer and the CNT phases. For the interface, two interfacial properties, viz., interfacial strength and fracture energy have been included. To account for variable temperature and strain rate over the deformation zone during machining, temperature and strain rate-dependent mechanical properties for the interface and the polymer material have also been included in the model. It is found that the FE machining model predicts cutting force within 6% of the experimental values at different machining conditions and CNT loadings. The cutting force data reveals that the model can accurately capture the CNT pull-out/protrusion, and the subsequent surface damage. Simulated surface damage characteristics are supported by the surface topographies and roughness values obtained from the machining experiments. The study suggests that the model can be utilized to design the new generation of CNT-polymer composites with specific interfacial properties that minimize the surface/subsurface damage and improve the surface finish.