Gully-type gangue dumps face critical stability challenges under complex geometric-hydrogeological coupling effects. This study establishes a novel 3D limit equilibrium framework integrating with coefficient of variation and grey relational analysis, validated through the Baode Mine's No.1 gangue field. The methodology quantifies stability sensitivity to four governing parameters: gully slope angle, dump slope angle, groundwater level, and rainfall infiltration depth. Key findings reveal: (1) gully slope angles dominate stability, where 10° increases from 25° to 35° reduce stability coefficients by 19.3–24.8% with exponential failure probability growth; (2) Dual-method sensitivity analysis consistently identifies gully slope > dump slope > groundwater level > rainfall infiltration as the critical hierarchy; (3) Engineering thresholds mandate gully basal slope angles ≤ 25°, groundwater levels < 10 m, and infiltration barriers for rainfall < 4 m. The proposed 3D approach resolves spatial confinement effects unattainable by 2D methods, providing a validated protocol for global mining gangue management.