This study simulates the cutting of epoxy-based material with the Mulliken-Boyce constitutive model using the Abaqus package. Two sizes of simulation models were established to represent micro- and macro-machining processes. The formation of epoxy chips is investigated under various finite element cutting conditions. It is found that the continuous, serrated, and broken epoxy chip types found in previous experiments can be realised via this simulation method. It is demonstrated that the machining of epoxy controlled by local deformation should be classified as a shear plastic slip mechanism consistent with experimental results. This simulation can be used to guide industrial production to achieve improvements in manufacturing.