Point cloud registration is challenging in the presence of heavy outlier correspondences. This paper focuses on addressing the robust correspondence-based registration problem with gravity prior that often arises in practice. The gravity directions are typically obtained by inertial measurement units (IMUs) and can reduce the degree of freedom (DOF) of rotation from 3 to 1. We propose a novel transformation decoupling strategy by leveraging the screw theory. This strategy decomposes the original 4-DOF problem into three sub-problems with 1-DOF, 2-DOF, and 1-DOF, respectively, enhancing computation efficiency. Specifically, the first 1-DOF represents the translation along the rotation axis, and we propose an interval stabbing-based method to solve it. The second 2-DOF represents the pole which is an auxiliary variable in screw theory, and we utilize a branch-and-bound method to solve it. The last 1-DOF represents the rotation angle, and we propose a global voting method for its estimation. The proposed method solves three consensus maximization sub-problems sequentially, leading to efficient and deterministic registration. In particular, it can even handle the correspondence-free registration problem due to its significant robustness. Extensive experiments on both synthetic and real-world datasets demonstrate that our method is more efficient and robust than state-of-the-art methods, even when dealing with outlier rates exceeding 99%.