High groundwater levels can generate excessive uplift pressure beneath canal linings, causing heaving, cracking, and sliding failure. This study developed a multi-objective framework for relief-well dewatering design in a damaged reach of the headrace canal at the HLJ Hydropower Station. A three-dimensional finite-element seepage model, validated using field-monitoring data under a cross-condition validation framework, was combined with a Box–Behnken design and response surface methodology to quantify the effects of relief-well location, spacing, and depth to the pumping control water level on the relative uplift pressure head and pumping rate. NSGA-II was used to generate Pareto-optimal solutions considering hydraulic safety, number of relief wells, and total pumping demand. Hydraulic conductivity sensitivity analysis showed that the sand–gravel layer had the greatest influence on uplift pressure. The maximum adverse head increment of 0.0047 m was adopted as a hydraulic-conductivity sensitivity margin, resulting in a sensitivity-adjusted screening threshold of 0.2253 m. Entropy-weighted TOPSIS identified a compromise design with a well-to-canal-edge distance of 1.95 m, a spacing of 38.8 m, a depth to the pumping control water level of 8.36 m, and 32 relief wells. Monte Carlo weight sensitivity analysis indicated that the TOPSIS ranking was stable under moderate weight variations but became more sensitive at larger perturbations. Finite-element verification yielded a relative uplift pressure head of 0.2232 m and a total pumping rate of 0.3462 m³/s, with the verified head remaining below the sensitivity-adjusted screening threshold and the selected scheme providing a reasonable balance among uplift-pressure control, construction scale, and pumping demand.