The unsatisfied effects of point cloud classification and segmentation caused by insufficient geometric feature extraction and high-level semantic feature loss in deep learning-based point cloud processing methods are problematic. Hence, this study proposes a point cloud classification and segmentation network based on topological awareness and channel attention to address these issues. The proposed method improves the precision of point cloud classification and segmentation from information amplification and feature enhancement. First, for the weak expression of low-level geometric features caused by the point cloud data being disordered, the topological relationships between the point cloud data and their neighborhood points are constructed using the local minimum triangulation strategy. Then, the residual multilayer perceptron module is applied to extract more granular local geometric information. Finally, the mixed pooling strategy is exploited for the feature aggregation of local information, and the channel affinity attention mechanism is used to reduce the feature loss in the network. Extensive comparative experiments are conducted on the ModelNet40 dataset, ScanObjectNN dataset, ShapeNet Part dataset, and S3DIS dataset. Using the proposed method, overall accuracy values of 93.6% and 85.6% are achieved in a classification task. Moreover, average crossover ratio values of 85.8% and 63.7% of are achieved in a segmentation task. Therefore, the experimental results demonstrate that the proposed method displays state-of-the-art performance in both point cloud classification and segmentation tasks.