Understanding of the ultraprecision diamond turning of polymethyl methacrylate (PMMA) is challenged by its complex strain-rate- and temperature-dependent mechanical behavior. To address this issue, a quasi-two-dimensional finite element method model using a coupled Eulerian–Lagrangian (CEL) approach in Abaqus/Explicit is developed and validated in this work. A key innovation is a pragmatic, data-driven material model generated from a comprehensive library of digitized stress–strain curves, which effectively captures the thermomechanical properties of PMMA without relying on complex constitutive laws. The CEL formulation successfully manages the large material deformation and continuous chip formation inherent to the cutting process. Model predictions for cutting forces $(F_{\text{c}})$, thrust forces $(F_{\text{p}})$, and chip thickness $(t_{\text{chip}})$ are rigorously compared against experimental data from a series of orthogonal cutting tests with varying depths of cut $(a_{\text{p}})$ and cutting speeds $(v_{\text{c}})$. The simulation demonstrated strong qualitative agreement with the experimental trends, confirming its ability to capture the underlying process physics and providing a robust, validated foundation for the optimization of the diamond turning process for amorphous polymers in high-precision applications.