Tailings storage facility (TSF) site selection requires the simultaneous consideration of economic, engineering, safety, and social factors. Taking a copper-polymetallic mine in northern China as an engineering case, this study develops a feasibility-stage decision-support framework combining the analytic hierarchy process (AHP) and the technique for order preference by similarity to an ideal solution (TOPSIS) to evaluate six pre-screened candidate sites using 11 indicators. The relative closeness coefficients of Schemes I–VI were 0.5345, 0.4996, 0.4949, 0.3543, 0.4407, and 0.6125, respectively, resulting in the ranking VI > I > II > III > V > IV. Scheme VI was therefore identified as the preferred alternative. Robustness analyses considering weight uncertainty, ordinal-indicator coding, normalization, and alternative ranking procedures generally preserved the preferred-site identification; Scheme VI ranked first in 99.31% of 100,000 Monte Carlo simulations, and MOORA and EDAS produced the same complete ranking as TOPSIS. The ranking was also consistent with the project feasibility-study recommendation. The study provides a transparent and robustness-oriented workflow for comparative TSF site selection at the feasibility stage rather than proposing a new MCDM algorithm.