Methane hydrates, as a potential energy resource for the future, remain a considerable interest in the field of geoenergy and geo-resources. However, there is still a challenge to accurately characterize the coupled multiphysics during the entire exploitation process, specifically when involving sand production and sand control. In this study, an innovative semi-analytical model is developed to fully consider the coupled interactions between sand migration and multiphysics (seepage, temperature, hydrate dissociation, and mechanical behaviors) around a vertical production well. Furthermore, the mud cake formed near the screen is also taken into consideration. Meanwhile, the influence of reservoir deformation, hydrate dissociation, and hydraulic drag on sand production are taken into account in the current coupled multiphysics framework. Additionally, the effect of solid particle detachment on the mechanical properties of the formation and the effect of solid mass variation on the permeability and porosity of the reservoir, etc., , are fully considered. As a step of validation, a good agreement is observed for gas production and sand production, between the presented solutions and field measurements. Based on the proposed solutions, depressurization-driven exploitation problems are analyzed for different cases, meanwhile, recommendations for engineering applications are presented from the perspectives of engineering safety, efficiency, and sustainability.