Recently, 3D point cloud classification has made significant progress with the help of many datasets. However, these datasets do not reflect the incomplete nature of real-world point clouds caused by occlusion, which limits the practical application of current methods. To bridge this gap, we propose ModelNet-O, a large-scale synthetic dataset of 123,041 samples that emulates real-world point clouds with self-occlusion caused by scanning from monocular cameras. ModelNet-O is 10 times larger than existing datasets and offers more challenging cases to evaluate the robustness of existing methods. Our observation on ModelNet-O reveals that well-designed sparse structures can preserve structural information of point clouds under occlusion, motivating us to propose a robust point cloud processing method that leverages a critical point sampling (CPS) strategy in a multi-level manner. We term our method PointMLS. Through extensive experiments, we demonstrate that our PointMLS achieves state-of-the-art results on ModelNet-O and competitive results on regular datasets such as ModelNet40 and ScanObjectNN, and we also demonstrate its robustness and effectiveness. Code available: https://github.com/fanglaosi/ModelNet-O_PointMLS.