Terahertz (THz) waves exhibit distinctive advantages for biomedical sensing, while metasurface technology offers an effective route toward high-performance THz sensors. A high-sensitivity THz metasurface absorber sensor for biological sample detection is proposed and numerically investigated. The sensor adopts a metal-insulator-metal (MIM) configuration, in which four centrosymmetrically arranged split metal rings form a multimode resonator. Copper is employed as the metallic layer, and PTFE is selected as the dielectric spacer. The electromagnetic response of the sensor is analyzed using CST Microwave Studio based on the FIT. Simulation results demonstrate that the proposed sensor supports two independent near-perfect absorption resonances at 3.1564 THz and 3.724 THz, with peak absorption rates of 99.75% and 99.84%, respectively. Owing to the strong localized field enhancement and multimode coupling effects, the resonant frequencies exhibit pronounced sensitivity to variations in the surrounding refractive index. Within the typical refractive-index range of biomedical samples, the maximum sensitivity reaches 241 GHz/RIU, accompanied by a maximum figure of merit (FOM) of 8.02. In addition, the absorption performance remains above 99% for polarization angles from 0° to 90°, with negligible resonance shift, indicating excellent polarization insensitivity. Benefiting from the use of low-dielectric-constant materials, the proposed sensor showed good material compatibility and portability. These results suggested that the designed metasurface absorber provided a promising platform for high-sensitivity terahertz biosensing applications.