With the rapid development of China’s economy, the construction of infrastructure has continuously improved. In the past few years, the construction of water conservancy projects has been constantly developing, and related geological disasters have become increasingly prominent. The stability of water conservancy slopes is related to whether water conservancy projects can be safely constructed and built to function safely and effectively, which has become a topic of increasing concern for geologists and related researchers. This paper selects the Jinping 1 Hydropower Station in Sichuan, China, for analysis. Four categories of evaluation factors (geological, engineering, environmental, and monitoring) and 24 subfactors (17 quantitative indicators and 7 qualitative indicators) are selected to ascertain the risk of the slope more accurately. By investigating the deficiencies of the traditional cloud model, the related concepts and computational models of a finite-area cloud model are proposed. By obtaining the characteristic parameters, the degrees of membership of the measurement samples belonging to different risk levels are further obtained. The weights of the indicators determined by the cloud processor and the weighted distance discriminant method are used to determine the final weights and achieve a final classification of the slope stability level. The research results demonstrate that the weighted distance discriminant algorithm combined with the improved finite-interval cloud model can consider the comprehensive information of each evaluation index and the degrees of mutual influence between the indicators, making the evaluation results more objective. Moreover, the proposed approach can quickly and accurately classify slope stability and deliver a prediction of the safety, thereby providing new ideas for evaluating the stability of slopes.