3D point cloud is a three-dimensional data format generated by LiDARs and depth sensors, and is being increasingly used in a large variety of applications. This paper presents a novel solution called SEmantic Point cloud Transmission (SEPT), for the transmission of point clouds over wireless channels with limited bandwidth. At the transmitter, SEPT encodes the point cloud via an iterative downsampling and feature extraction process. At the receiver, SEPT reconstructs the point cloud with latent reconstruction and offset-based upsampling. Extensive numerical experiments confirm that SEPT significantly outperforms the standard approach with octree-based compression followed by channel coding. Compared with a more advanced benchmark that utilizes state-of-the-art deep learning-based compression techniques, SEPT achieves comparable performance while eliminating the cliff and leveling effects. Thanks to its improved performance and robustness against channel variations, we believe that SEPT can be instrumental in collaborative sensing and inference applications among robots and vehicles, particularly in the low-latency and high-mobility scenarios.