Pre-existing concealed goafs underneath open-pit slopes (PCO-goafs) pose a serious threat to the stability of open-pit slopes (OP-slopes), which is a common problem worldwide. In this paper, the variable weight-target approaching method, equilibrium beam theory, Pratt’s arch theory, and numerical simulation are used to analyze the management solutions and stability of five PCO-goaf groups in the Nannihu molybdenum mine located in Luoyang City, Henan Province, China. The five PCO-goaf groups, numbered 1#, 2#, 3#, 4#, and 5#, are divided into four hazard classes, ranging from extremely poor to good stability. The stability of 1#, 2#, and 4# is poor and must be managed by filling, and the design strength of backfill is 1.2 MPa; caving is used to treat 3# and 5#, and the safe thickness of the overlying roof is calculated to be 10.5–41 m. After treatment, the safety coefficient of the slope is greater than 1.2, indicating that the slope is stable. This study provides insight and guidance for the safe operation of open-pit mines threatened by the existence of PCO-goafs.