The Element-Free Galerkin method (EFG) is a prominent member of the meshfree methods family. In this work, EFG is utilised to simulate the orthogonal cutting process of unidirectional composites. The mathematical model is derived from the weak form of the momentum conservation equation with frictional contact constraints based on penalty method. Spatial discretisation using moving least squares shape functions are used. The onset and progression of damage are predicted by two stress-based failure criteria. Full Newton Raphson solver is used to solve the non-linear system equations iteratively. Numerical experiments investigating the effect of rake angle and fibre orientation are conducted. Cutting forces are compared against experiments and finite element simulations available in literature. Simulations show that the meshfree model is capable of predicting cutting forces as a function of the fibre orientation. Sensitivity analysis is conducted to investigate the effect of important meshfree parameters such as the domain of influence and weight function on forces. One of the strongest advantages of the proposed model is the simple and automatic set up process, as meshing for domain discretisation is not required.