Deep-sea natural gas hydrates represent a vast energy frontier, yet commercial extraction triggers complex multiphysics couplings, posing significant geomechanical and environmental hazards. This perspective synthesizes recent advances in elucidating multiscale triggers of reservoir instability and gas leakage. Leveraging three-dimensional digital rock physics, the impact of microstructural evolution on nonlinear flow is investigated, with specific focus on hydrate morphology transitions and fines-migration-induced clogging. Geomechanical hazards are interpreted through novel stress-partitioning constitutive models coupled with acoustic-mechanical monitoring. Furthermore, the integration of multidimensional geophysical monitoring with hybrid data-driven and physics-based fusion methodologies offers a novel pathway for predicting coupled hydro-mechanical behaviors and enables real-time adaptive management. By bridging the scale gap from molecular kinetics to reservoir-scale responses, a comprehensive framework is outlined for safe and predictable hydrate production while mitigating environmental leakage risks.