We report terahertz surface plasmon resonance (SPR) sensing based on prism-coupling to the spoof surface plasmon polariton (SSPP) mode existing on periodically grooved metal films. It was demonstrated that, except for the fundamental mode of the SSPP, there was also a higher mode SSPP wave when the depth of groove was larger. Both fundamental and high-order modes of SSPP could be used for terahertz sensing. We compared the performance of different modes of SSPP on the sensing sensitivity using both reflection amplitude and phase-jump information. The results indicated that the gap distance between the prism base and the metal film had a significant influence on the reflectivity of SPR sensing by affecting the coupling efficiency of an evanescent wave to an SSPP wave; also, high-order mode SSPP-based sensing had a high sensitivity of up to 2.27 THz/RIU, which nearly doubled the sensitivity of the fundamental mode. The application of high-mode SSPP has enormous potential for ultra-sensitive SPR sensing in the terahertz regime.