To investigate the influence of a geogrid-reinforced tailings dam on the seepage stability of the dam body, this paper was based on the field test of a reinforced tailings accumulation dam. The study utilized the finite element strength reduction method to simulate the stability of the main dam of the Fengshuigou tailings reservoir under different seepage conditions using ABAQUS software. Additionally, the paper discussed the impact of conventional heightening, dry beach length, and geogrid reinforcement on the position and safety factor of the saturation line of the dam body. The results showed that when the dam body was raised, the saturation line rose by 2.8–5.3 m, resulting in a decrease in the safety factor. The geogrid effectively reduced the height of the saturation line in the tailings dam. In comparison to the unreinforced condition (dam heightening), the saturation line of the tailings dam decreased by 0.9–2.8 m under the local reinforcement condition and by 3.2–12.5 m under the overall reinforcement condition. The geogrid significantly improved the stability of the tailings dam. Furthermore, under the local reinforcement condition, the safety factor of the dam increased by 3.8–5.5%, and under the overall reinforcement condition, it increased by 35.9–42.9%, when compared to the unreinforced condition. Increasing the dry beach length improved the stability of the tailings dam, and under normal working conditions, the safety of the tailings dam was much higher than under the minimum dry beach condition. These results served as a reference for the design of the dam and the new tailings reservoir, laying a foundation for the sustainable development and environmental protection of the tailings pond.