Glassy polymers exhibit highly nonlinear viscoplastic behavior under large deformation, which poses significant challenges for conventional constitutive modeling. This work presents a mechanism-based data-driven viscoplastic (MDVP) framework that tightly integrates artificial intelligence with computational mechanics for efficient and physically consistent material modeling. The formulation is derived from the principle of virtual work and energy balance, ensuring thermodynamic consistency. A joint training strategy based on two coupled neural networks is proposed to automatically learn both the back-stress evolution law associated with molecular orientation hardening and the plastic flow rule. Physical constraints are explicitly embedded into the learning process, enabling the model to preserve essential mechanical principles while achieving strong predictive capability with limited training data. The MDVP model has been implemented into commercial finite element software and validated through representative numerical examples, demonstrating its ability to accurately capture complex nonlinear responses of glassy polymers under diverse loading conditions. Furthermore, we introduce Chat-Mechanics, a computational mechanics framework that couples large language models with data-driven constitutive modeling, enabling natural-language-driven construction and interaction with constitutive models. This paradigm offers a new pathway toward intelligent, interactive, and data-efficient material modeling.