Data augmentation is developed for increasing the amount and diversity of training data to enhance model learning. Compared to 2D images, point clouds, with the 3D geometric nature as well as the high collection and annotation costs, pose great challenges and potentials for augmentation. This paper presents a 3D augmentation method that explores the structural variance across multiple point clouds, and generates more diverse point clouds to enrich the training set. Specifically, we propose an attention module that decomposes a point cloud into several disjoint point subsets, called divisions, in a way where each division has a corresponding division in another point cloud. The augmented point clouds are synthesized by swapping matched divisions. They exhibit high diversity since both intra- and inter-cloud variations are explored, hence useful for downstream tasks. The proposed method for augmentation can act as a module and be integrated into a point-based network. The resultant framework is end-to-end trainable. The experiments show that it achieves state-of-the-art performance on the ModelNet40 and ModelNet10 benchmarks. The code for this work is publicly available (The source code is available at: https://github.com/ardianumam/PointMixSwap ).