Accurate identification of discontinuities is essential for rock mass stability analysis. With the development of remote sensing technologies, non-contact measurement has become a mainstream approach. In this regard, this paper presents a new method to identify rock discontinuities from 3D point clouds that balances accuracy and efficiency. The proposed method first applies the k-nearest neighbor (KNN) search algorithm and principal component analysis (PCA) to calculate the normal vectors. Based on the calculated roughness values, edge and sharp regions are discarded. Clustering seed points are generated by uniform downsampling method, and the multipoint clustering algorithm (MPC) is developed to recognize individual discontinuities from the point clouds. The random sample consensus (RANSAC) algorithm is applied to determine the orientation of the discontinuities, and an improved self-organizing map (SOM) neural network is used to group the discontinuity sets. Finally, the performance of the new method is evaluated via three real-world cases. The research results demonstrate that the proposed method can accurately identify discontinuities from outcrop rock mass, with the error being within 3° compared to manual measurement. Moreover, the computational efficiency of the new method is several times faster than that of previous research methods. The new method can be used to recognize rock discontinuities from large-scale 3D point clouds.