Category-level object pose estimation involves estimating the 6D pose and the 3D metric size of objects from predetermined categories. While recent approaches take categorical shape prior information as reference to improve pose estimation accuracy, the single-stage network design and training manner lead to sub-optimal performance since there are two distinct tasks in the pipeline. In this paper, the advantage of two-stage pipeline over single-stage design is discussed. To this end, we propose a two-stage deformation-and registration pipeline called DR-Pose, which consists of completion-aided deformation stage and scaled registration stage. The first stage uses a point cloud completion method to generate unseen parts of target object, guiding subsequent deformation on the shape prior. In the second stage, a novel registration network is designed to extract pose-sensitive features and predict the representation of object partial point cloud in canonical space based on the deformation results from the first stage. DR-Pose produces superior results to the state-of-the-art shape prior-based methods on both CAMERA25 and REAL275 benchmarks. Codes are available at https://github.com/Zray26/DR-Pose.git.