The recent trend in deep learning methods for 3D point cloud understanding is to propose increasingly sophisticated architectures either to better capture 3D geometries or by introducing possibly undesired inductive biases. Moreover, prior works introducing novel architectures compared their performance on the same domain, devoting less attention to their generalization to other domains. We argue that the ability of a model to transfer the learnt knowledge to different domains is an important feature that should be evaluated to exhaustively assess the quality of a deep network architecture. In this work we propose PatchMixer, a simple yet effective architecture that extends the ideas behind the recent MLP-Mixer paper to 3D point clouds. The novelties of our approach are the processing of local patches instead of the whole shape to promote robustness to partial point clouds, and the aggregation of patch-wise features using an MLP as a simpler alternative to the graph convolutions or the attention mechanisms that are used in prior works. We evaluated our method on the shape classification and part segmentation tasks, achieving superior generalization performance compared to a selection of the most relevant deep architectures.