In this work, we apply the Particle Finite Element Method (PFEM) and Smoothed Particle Hydrodynamics (SPH) to simulate the orthogonal cutting chip formation of two workpiece materials, i.e., AISI 1045 steel and Ti6Al4V titanium alloy. A modified Johnson–Cook constitutive model is used to model the plastic behavior of the two workpiece materials. No damage or strain softening is included in the model. The friction between the workpiece and the tool is modeled following Coulomb’s law with a temperature-dependent coefficient. The accuracy of PFEM and SPH in predicting thermomechanical loads at various cutting speeds and depths against the experimental data are compared. The results show that both numerical methods can predict the rake face temperature of AISI 1045 with errors less than 34%. For Ti6Al4V, however, the temperature prediction errors are significantly higher than those of the steel alloy. Errors in force prediction were in the range of 10% to 76% for both methods, which compare very well with those reported in the literature. This investigation infers that the Ti6Al4V behavior under machining conditions is difficult to model on the cutting scale irrespective of the choice of numerical method.