Abstract: Slope stability is the basis of mine safety production. It is of great theoretical and practical significance to study the sensitivity order of influencing factors of slope stability. In this paper, a sensitivity ranking theory based on CRITIC-GRA-AHP method is proposed to overcome the shortcomings of single subjective algorithm which is greatly influenced by subjectivity and single objective algorithm which has a large deviation from the actual situation on site and can only analyze specific working conditions. Taking a limestone mine in northwest Sichuan as an example, on the basis of analyzing and determining the influencing factors of slope stability such as slope height, slope angle, rock mass gravity, rock mass cohesion and internal friction angle of rock mass, the sensitivity of influencing factors of mine slope stability is analyzed by FLAC3D combined with the sensitivity ranking theory based on CRITIC-GRA-AHP combined algorithm. The results show that the sensitivity order of slope stability influencing factors under natural conditions, rainstorm conditions and earthquake conditions is as follows: (1) Under natural conditions: internal friction angle, slope height, cohesion, slope angle, gravity and bulk modulus; (2) Rainstorm conditions: internal friction angle, cohesion, slope height, gravity, slope angle, bulk modulus; (3) Under seismic conditions: internal friction angle, slope height, cohesion, slope angle, unit weight, bulk modulus. The sensitivity of influencing factors of slope stability under rainstorm conditions is stronger than that of earthquake conditions, and the sensitivity of influencing factors of slope stability under earthquake conditions is stronger than that of natural conditions. On this basis, the cloud model theory is used to optimize the overall slope angle of the slope. Finally, it is determined that the overall angle of the mine slope is 51°, which is consistent with the actual situation of the mine. The research results of this paper can provide reference for similar mine slope disaster prediction and prevention and subsequent engineering treatment.