The biomass components of the invasive seaweed Sargassum muticum were fractionated to allow their separate valorization. S. muticum (Sm) and the solid residue remaining after alginate extraction of this seaweed (AESm) were processed with hot, compressed water (hydrothermal processing) to assess the effects of temperature on fucoidan solubilization. Fucose-containing oligosaccharides were identified as reaction products. Operating under optimal conditions (170 °C), up to 62 and 85 wt% of the dry mass of Sm and AESm were solubilized, respectively. The reaction media were subjected to precipitation, nanofiltration and freeze-drying. The dried products contained 50% and 85% of the fucoidan present in Sm and AESm, respectively; together with other components such as phenolics and inorganic components. The saccharidic fraction, accounting for up to 35% of the dried extracts, contained fucose as the main sugar, and also galactose, xylose, glucose and mannose. The concentrates were characterized for antioxidant activity using the TEAC assay.