Multi-instance point cloud registration is crucial for various 3D computer vision tasks but presents significant challenges, including an unknown number of instances, severe occlusions, background clutter, and object similarity. Traditional methods often struggle with computational efficiency or, like some recent end-to-end approaches, may overlook detailed geometric cues inherent in the spatial data, hindering disambiguation in complex scenes. This paper introduces the Geometric Self-Attenuating Transformer (GSAT), a novel architecture designed to address these limitations by robustly encoding superpoint features. GSAT employs a dual-branch local attention mechanism that explicitly processes both geometric and contextual information within each instance, enhancing feature discriminability. Crucially, a Geometric Self-Attenuation Mechanism (GSAM) adaptively regulates the influence of an anchor superpoint’s self-derived geometric information when processing scene point clouds, mitigating contamination caused by occlusion and inter-instance interference. Experiments on the ROBI and Scan2CAD datasets demonstrate that GSAT achieves competitive performance compared to state-of-the-art methods, highlighting its effectiveness in handling complex real-world scenarios.