The recovery of biopolymers from natural resources using eco-friendly extraction technologies that enhance their mechanical properties has gained attention in recent years. In this context, this work deals with the isolation of hybrid carrageenans from Mastocarpus stellatus red seaweed using subcritical water extraction operating in a wide range of thermal conditions (70–190 °C). The extracted biopolymers were analyzed by means of either Fourier-Transform infrared, nuclear magnetic resonance, rheological or cell viability assays. In parallel, the fundamental chemical composition of the seaweed used as raw material, as well as the main phytochemical properties of the soluble liquid extracts, were also studied. Results indicated that thermal extraction conditions significantly affected the rheological behavior of the recovered hybrid carrageenans. The hybrid carrageenan extraction yields varied, with results between 10.2 and 30.2% being the highest values obtained at hydrothermal treatment of 130 °C. A wide palette of viscous features was identified for recovered hybrid carrageenans, with the strongest rheology properties observed at the same temperature. It should be remarked that the maximum inhibitory effect was also obtained at 130 °C for both the ovarian carcinoma cell line (A2780) (65%, IC50: 0.31 mg/mL) and lung carcinoma cell line (A549) (59%, IC50: 0.41 mg/mL).