Elucidating the multi-field, multi-phase coupling mechanisms in submarine hydrate reservoirs is essential for releasing their energy potential. Current research gaps remain in understanding the permeability-stress coupling characteristics of hydrate reservoirs. This study conducted permeability-stress coupling tests on hydrate-bearing clayey-silty sediments (HBCS). The seepage characteristics and mechanical response of HBCS under seepage-stress coupling effects were investigated. The results indicate that under stress conditions, the seepage flow of HBCS follows a logarithmic relationship with axial strain, with its rate of increase decelerating as axial strain grows. Apparent permeability decreases rapidly at first and then more gradually with increasing axial strain. Hydrate saturation (Sh) and seepage pressure difference (PS) exhibit a coupling effect on apparent permeability. At low-Sh levels, particle migration induced by seepage reduces permeability. At high-Sh levels, permeability is affected by two competing mechanisms (pore expansion and particle migration) driven by seepage forces. Unlike triaxial tests for HBCS, under seepage conditions, the plastic deformation capacity of HBCS is enhanced. The stress-strain curve exhibits strain hardening and plastic flow, and lacks obvious strain softening. Shear strength decreases with increasing Sh and PS, while the secant modulus E50 rises with both parameters. During hydrate exploitation, production efficiency correlates with Sh. In low-Sh reservoirs, a “slow and steady” production strategy is recommended to prevent sand production and wellbore blockage. In high-Sh reservoirs, increasing PS can promote pore expansion and fracture propagation, thereby enhancing production efficiency. This study provides a reference for engineers to understand the multi-field and multi-phase coupling characteristics during the exploitation of hydrate reservoirs.