The development of greener processes for the sustainable utilization of raw materials is increasingly demanded for environmental and economic reasons. A rapid and chemical-free technique was proposed for the extraction of hybrid kappa/iota (6/4) carrageenan from Sarcopeltis (ex Gigartina) skottsbergii. After separation, carrageenans were analyzed by Fourier transform infrared attenuated total reflectance, high-performance size-exclusion chromatography, and rheology. Maximum carrageenan extraction yields up to 63–64% were obtained operating at 110 or at 160 °C, for 5–7 min considering the sum of the heating and cooling periods, but the extraction of the phenolic fraction was favored at 220 °C. The recovered carrageenan showed apparent viscous values around 103 mPa at the lowest tested shear rates (0.1 1/s) and could be suitable to formulate films. Furthermore, those carrageenans obtained under 140 °C showed gel characteristics without previous separation from the liquid extract, avoiding ethanolic precipitation and energy consumption. The antiradical properties correlated with the phenolic content in the liquid phase, but no influence of temperature on the reducing properties was observed. The microwave-assisted hydrothermal treatment could be an efficient tool without needing chemicals for the extraction of carrageenans, which showed adequate rheological properties for commercial uses.