Point cloud registration is important in computer-aided interventions (CAI). While learning-based point cloud registration methods have been developed, their clinical application is hampered by issues of generalizability and explainability. Therefore, classical point cloud registration methods, such as Iterative Closest Point (ICP), are still widely applied in CAI. ICP methods fail to consider that: (1) the points have well-defined semantic meaning, in that each point can be related to a specific anatomical label; (2) the deformation needs to follow biomechanical energy constraints. In this paper, we present a novel semantic ICP (sem-ICP) method that handles multiple point labels and uses linear elastic energy regularization. We use semantic labels to improve the robustness of the closest point matching and propose a new point cloud deformation representation to apply explicit biomechanical energy regularization. Our experiments on the Learn2reg abdominal MR-CT registration dataset and a trans-oral robotic surgery ultrasound-CT registration dataset show that our method improves the Hausdorff distance compared with other state-of-the-art ICP-based registration methods. We also perform a sensitivity study to show that our rigid initialization achieves better convergence with different initializations and visible ratios.