The rising demand for liquefied natural gas (LNG) has spurred research into offshore regasification platforms as a reliable solution to meet global energy needs. Buoyant leg storage and regasification platforms (BLSRPs) offer superior positional stability compared to ship-shaped alternatives; however, heave motion needs to be mitigated for safe regasification. This study proposes a semi-active response control mechanism (RCM) employing magnetorheological (MR) dampers to suppress radial buoyant leg displacements, which are directly coupled with deck heave. A baseline numerical model of the BLSRP was developed in AQWA software without an RCM, and a mathematical model incorporating the MR-RCM was formulated to evaluate the controlled system performance. Unlike previous BLSRP studies, we explicitly incorporated combined wave–wind–current environmental loading conditions. Transformation matrices were established to convert radial responses into deck heave, with influence factors calibrated for varying sea states and approach angles. Results indicate that the MR-RCM achieves 30–45% root-mean-square reductions in radial displacements under moderate and high sea conditions, resulting in significant control of deck heave. Even under very high sea states, 8–11% reductions are maintained, preventing uncontrolled escalation. Hysteresis plots validate the nonlinear energy dissipation of MR dampers and their adaptability to broadband excitations. The findings demonstrate that MRRCM improves platform stability, reduces boil-off gas generation, and enhances safety in LNG operations. Overall, the study establishes MR-based semi-active damping as a practical and scalable solution for offshore platforms, bridging the limitations of passive devices and the complexities of fully active systems.