Point cloud registration plays a crucial role in computer vision and robotics. In recent years, although a series of registration methods have achieved remarkable success in terms of accuracy and efficiency, few studies have thoroughly investigated the impact of feature interactions across different scales on registration performance. We propose a multi-scale masked autoencoding geometric transformer, which achieves high-precision registration through hierarchical feature fusion. The method innovatively employs a multi-scale masking strategy to construct cross-scale consistent visible regions. During the encoding phase, it simultaneously models intra-point-cloud structural features and inter-point-cloud geometric consistency via a dual-branch attention mechanism. In the decoding stage, a feature pyramid fusion module is designed to progressively aggregate low-level geometric details and high-level semantic features through skip connections. Finally, a deep regressor is utilized to supervise and optimize the matching between predicted values and ground truth, enabling robust point correspondence. Experiments demonstrate that MMGT achieves superior performance on both 3DMatch and KITTI datasets.