To address the neglect of real-time mass transfer effects by traditional analysis methods during the side-by-side offloading process of Floating Production Storage and Offloading (FPSO) and shuttle tankers, a numerical model incorporating the variable mass effect is established to enable the simulation of dynamic offloading processes. Using this model, the dynamic response characteristics under different offloading rates and sea conditions are systematically investigated and validated against towing tank tests. Based on the previously optimized benchmark configuration, which includes 16 side-by-side mooring lines, six floating fenders, and an anchor line angle of 60° for the FPSO, the evolution laws of mooring line tension and fender pressure under different offloading rates were systematically investigated under normal and extreme sea conditions. The results show that an increase in offloading rate significantly amplifies the system’s fender load; when the offloading rate reaches approximately 1.4 t/s, the system transitions from the quasi-static response region to a significant nonlinear coupling region, demonstrating obvious sea condition–rate coupling characteristics. Under the combined action of high offloading rates and severe sea conditions, fender pressure rapidly approaches the design limit, becoming the primary safety bottleneck for the system. Model test results indicate that the numerical model can well predict mechanical responses under low and medium offloading rate conditions. The research results can provide a reference for offloading rate control, safety assessment, and operational window determination during FPSO side-by-side dynamic offloading operations.