This research focuses on the study of the simulation capabilities of the lagrangian (LAG) model and Smoothed Particle Hydrodynamics (SPH) model for the orthogonal dry machining of aluminum alloy Al6061-T6. A three-dimensional finite element model was developed and verified using experimental data from the published literature. The numerical models were developed using lagrangian boundary conditions via finite element modeling in ABAQUS/Explicit 6.14. The cutting simulations were carried out at low and medium cutting speeds. Johnson–Cook material constitutive law and Johnson–Cook damage law were used in both models. The numerical methodologies are compared based on cutting forces, chip morphology, shear angle, chip separation criterion, and chip thickness. The findings of the present work show that the LAG model is good for predictions regarding cutting forces and chip morphology, while the SPH model is good for predictions regarding the shear angle and chip thickness. The difference between results generated by both models mainly occurred due to the friction coefficient. The comparative study shown here offers a guidance approach for various numerical models for appropriate parameter analysis.