The overtopping-induced lateral erosion breaching of tailings dams represents a critical disaster mechanism threatening structural safety, particularly in reinforced fine-grained tailings dams where erosion behaviors demonstrate pronounced water–soil coupling characteristics and material anisotropy. Through physical model tests and numerical simulations, this study systematically investigates lateral erosion failure patterns of reinforced fine-grained tailings under overtopping flow conditions. Utilizing a self-developed hydraulic initiation test apparatus, with aperture sizes of reinforced geogrids (2–3 mm) and flow rates (4–16 cm/s) as key control variables, the research elucidates the interaction mechanisms of “hydraulic scouring-particle migration-geogrid anti-sliding” during lateral erosion processes. The study revealed that compared to unreinforced specimens, reinforced specimens with varying aperture sizes (2–3 mm) demonstrated systematic reductions in final lateral erosion depths across flow rates (4–16 cm/s): 3.3–5.8 mm (15.6−27.4% reduction), 3.1–7.2 mm (12.8–29.6% reduction), 2.3–11 mm (6.9–32.8% reduction), and 2.5–11.4 mm (6.2–28.2% reduction). Smaller-aperture geogrids (2 mm × 2 mm) significantly enhanced anti-erosion performance through superior particle migration inhibition. Concurrently, a pronounced positive correlation between flow rate and lateral erosion depth was confirmed, where increased flow rates weakened particle erosion resistance and exacerbated lateral erosion severity. The numerical simulation results are in basic agreement with the lateral erosion failure process observed in model tests, revealing the dynamic process of lateral erosion in the overtopping breach of a reinforced tailings dam. These findings provide critical theoretical foundations for optimizing reinforced tailings dam design, construction quality control, and operational maintenance, while offering substantial engineering applications for advancing green mine construction.