This paper addresses the privacy issue of 3D point clouds. Unlike existing 2D image privacy research, we focus on the 3D geometric structure of textureless 3D point clouds. We propose an efficient privacy-preserving framework called PointFlowGMM, which supports subsequent tasks such as classification and segmentation without access to the original data. Using a flow-based generative model, we project the point cloud into a latent Gaussian mixture distribution subspace. We then design a novel angular similarity loss function to obfuscate the original geometry and reduce the model size from 767 MB to 120 MB. The projected point cloud in the latent space is further protected through orthogonal rotation, and inter-class relationships are preserved even after rotation to support recognition tasks. We evaluated our approach on multiple datasets, achieving recognition results comparable to those of the original point cloud.