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. A novel SNR-adaptive module is proposed which allows the adaptive trained model to achieve comparable performance with the models trained and tested at different SNRs. 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.