Accurate registration of point clouds acquired from different viewpoints can effectively reconstruct three-dimensional scenes, which plays a crucial role in industrial applications. Many learning-based methods rely on the extracted point cloud features to find the correspondence between two point clouds and thus achieve point cloud registration. However, repetitive geometric structures can make the local features of the learned point clouds highly similar, leading to the generation of incorrect correspondences. We propose the Two-Stage Graph Matching Point Cloud Registration Network (TSGM-Net). First, we design a dynamic graph-to-point (DGTP) module to learn the feature representation of the local graph of the point cloud to improve the recognition of local features. Then, edges are dynamically established by the Transformer and the introduced edge threshold λ, and the graph attention network is used to extract global features of the point cloud to consider the relationship among similar features in the topological structure. At the same time, scores are calculated from the three dimensions of the node itself, local and global, and summed for keypoint detection. Finally, we propose a two-stage graph matching method, where keypoints with highly similar features are divided into different point groups, and the correspondences of the point groups are established in the first-stage graph matching. The correspondence of points in corresponding point groups is established in the second-stage graph matching, which in turn reduces the impact of similar features on the accuracy of point cloud registration. Based on the benchmark dataset, we evaluate the performance of TSGM-Net in four different scenarios. Experimental results show that TSGM-Net can better handle point clouds with repetitive geometric structures and is competitive with state-of-the-art methods.