Category-level 6D pose estimation plays a crucial role in the interaction between robots and the environment. Its purpose is to predict the pose information of unseen instances from known categories. The main challenge in the practical application is the significant shape variations among instances within the same category, making it difficult to accurately regress dense correspondences between reconstructed instance models and observed point clouds. Additionally, the current category-level grasping heavily relies on a large amount of manually annotated annotations for training, category-level pose estimation is rarely applied to grasping. In order to address these issues, we propose a joint framework that incorporates multi-stage reconstruction and grasp pose transfer. Specifically, it involves target feature encoder, multi-stage reconstruction, and grasp pose transfer. The target feature encoder initially builds an efficient dual-space point cloud network to encode the point cloud, avoiding interference from noisy points. Subsequently, it dynamically fuses geometric features, appearance features, and category shape prior features to provide robust features for subsequent tasks. Multi-stage reconstruction network predicts the residual of the initial reconstruction model and enhances the accuracy of dense correspondence matrix. Finally, to apply category-level 6D pose estimation to robot, we propose a grasp representation for the transfer of grasp pose within the same category, eliminating the need for extensive annotation. The experimental result indicates that the proposed method achieves good performance on the REAL275 and CAMERA25 datasets. We also applied this method to gripping experiments with the UR5 robotic arm, leading to an improvement in the grasping success rate.