Seabed characterisation consists in the study of the physical and biological properties of the bottom of the oceans. It is effectively achieved with sonar, a remote sensing method that captures acoustic backscatter of the seabed. Classical Machine Learning (ML) and Deep Learning (DL) research have failed to successfully address the automatic mapping of the seabed from noisy sonar data. This work introduces the Deep Supervised Semantic Segmentation model for Seabed Characterisation (D4SC), a novel U-Net-like model tailored to such data and low-label regime, and proposes a new end-to-end processing pipeline for seabed semantic segmentation. That dual contribution achieves state-of-the-art results on a high resolution Synthetic Aperture Sonar (SAS) survey dataset.