Additive Manufacturing (AM) has shown excellent research potential for biomedical implants, complex aerofoil structures, military applications, high-pressure cryogenic vessels, and automobile components. The mechanical properties exhibited by the additively manufactured Ti6Al4V ELI alloy components are significantly different from traditionally manufactured Ti6Al4V alloy due to the material anisotropy, orientation of the microstructure, and variation in heat treatments. Among AM techniques, SLM (Selective laser melting) offers unparalleled design flexibility with minimum impurities and high reproducibility. However, post-processing of additive manufactured components is essential due to their poor surface finish and lack of dimensional accuracy. Ti6Al4V ELI (Extra Low Interstitials) alloy is a difficult-to-cut material in Ultra-Precision Machining (UPM) due to its excessive tool wear, hardness, and chemical reactivity. Optimizing machining parameters for better surface finish by UPM is time-consuming and often not economical. Modeling and simulation provide a low-cost approach for the investigation of machining. In this work, a series of cutting experiments have been carried out on additively manufactured Ti6Al4V ELI alloy to study the cutting mechanism during UPM. In addition, Finite Element Model (FEM) is employed to understand the chip formation and cutting forces in UPM with a built-in Johnson-Cook (JC) model and a Johnson-Cook-TANH (JC-TANH) vectorized user-defined material subroutine (VUMAT) model. Cutting forces corresponding to the JC model and JC-TANH are examined with the experimental forces in literature, and the results are found to be fairly close.