As the technology of high-precision 3D laser scanning becomes increasingly prevalent in the fields of hydraulic building modeling and deformation monitoring, the quality of point clouds plays an increasingly crucial role in data processing. This paper investigates an automatic extraction method of anchor rod points based on geometric features, which focuses on the influence of anchor rod points and mixed pixels in the data of an underground powerhouse of a pumped storage power station on modeling and deformation monitoring during the construction period. This workflow consists of two steps that can automatically extract anchor rod points from high-density point cloud data. Triangular mesh features in the local neighborhood and the parameters of the anchor rods are used to locate the anchor rod in downsampled data, and curvature features are used to extract anchor rod points precisely. The experiment of extracting anchor rods shows that the accuracy of this method of initial identification is 97.2%. Furthermore, precise extraction based on curvature curve fitting is applicable. This method can accurately separate the three types of anchor rods from the dense point cloud on the rough surface of a cavern roof; the false-extraction rate of anchor rod points is about 0.11% to 5.09%. This method can provide high-quality and dependable data sources for the precise registration, modeling and deformation analysis of point clouds in a construction cavern.