This paper proposes BPNet, a novel end-to-end deep learning framework to learn Bézier primitive segmentation on 3D point clouds. The existing works treat different primitive types separately, thus limiting them to finite shape categories. To address this issue, we seek a generalized primitive segmentation on point clouds. Taking inspiration from Bézier decomposition on NURBS models, we transfer it to guide point cloud segmentation casting off primitive types. A joint optimization framework is proposed to learn Bézier primitive segmentation and geometric fitting simultaneously on a cascaded architecture. Specifically, we introduce a soft voting regularizer to improve primitive segmentation and propose an auto-weight embedding module to cluster point features, making the network more robust and generic. We also introduce a reconstruction module where we successfully process multiple CAD models with different primitives simultaneously. We conducted extensive experiments on the synthetic ABC dataset and real-scan datasets to validate and compare our approach with different baseline methods. Experiments show superior performance over previous work in terms of segmentation, with a substantially faster inference speed.