Rock slopes with inclined discontinuous joints are prevalent in practical engineering, and their stability and instability mechanisms are primarily controlled by the internal discontinuous structural planes and rock bridges of the slope. A generalized model for the high and steep rock slope of a hydropower station in the upper reaches of the Lancang River was established in this study. Based on the RFPA^3D-Centrifuge numerical simulation method and energy dissipation theory, the influences of parameters such as joint length, angle, and internal friction angle on the instability mechanism and stability of inclined discontinuous jointed rock slopes were systematically investigated. By analyzing the stress distribution, toe displacement, rock damage, microseismic events, and sliding surface connectivity during the slope instability process, the dominant role of joint parameters in slope instability modes was revealed. The research results indicate that joint length, angle, and internal friction angle are key factors affecting slope stability: the longer the joint length, the larger the joint angle, and the smaller the internal friction angle, the significantly higher the risk of slope instability; furthermore, the magnitude of the joint inclination angle significantly affects the slope’s instability mode. The formation of the sliding surface in intermittent jointed rock slopes is essentially a gradual failure process in which joints and rock bridges are gradually connected. Based on the simulation results, the slope instability process can be divided into three stages: the failure and connection of the lower rock bridges, the tensile fracture and connection of the rear edge of the upper rock bridges, and the overall instability due to the connection of the sliding surface. Intermittent joints play a dominant role in the instability process, and their connection direction and stress concentration effect significantly influence the slope’s stability and instability mode. A comparison between the theoretical calculation of the energy safety factor and the numerical simulation results shows that the RFPA3D Centrifuge method has good applicability in evaluating the stability of this type of slope. It can intuitively demonstrate the gradual instability process of the slope, thereby providing certain theoretical support for the stability analysis of jointed rock slopes.