Ground-based synthetic aperture radar (GB-SAR) is a relatively new technique that can be used to monitor the deformation of large-volume targets, such as dams, slopes, and bridges. In this study, the permanent scatterer (PS) technique is used to address the issues encountered in the continuous monitoring of the external deformation of an arch-gravity dam in a hydraulic and hydropower engineering structure in Hubei, China; the technique includes large image data sizes, high accuracy requirements, a susceptibility of the monitoring data to atmospheric disturbances, complex phase unwrapping, and pronounced decoherence. Through an in-depth investigation of PS extraction methods, a combined PS selection (CPSS) method is proposed by fully taking advantage of the signal amplitude and phase information in the monitored scene. The principle and implementation of CPSS are primarily studied. In addition, preliminarily selected PS candidates are directly used to construct and update a triangular irregular network (TIN) to maintain the stability of the subsequent Delaunay TIN. To implement this method, a differential-phase standard-deviation threshold method is proposed to extract PSs that are highly spatially coherent and consistent. Finally, the proposed CPSS was applied to the safety monitoring of the dam. The monitoring results are compared with conventional inverted plumb line monitoring results, and the proposed CPSS is found to be effective and reliable.