To achieve controllable excitation and precise manipulation of multiple terahertz Bound States in the Continuum (BIC) and explore their potential in sensing applications, this paper designs a novel symmetric metasurface structure. The formation and evolution mechanisms of multi-mode BICs are investigated through symmetry engineering. A metasurface structure based on concentric "square-inside-circular" metallic ring units is proposed. The influence of symmetry-breaking parameters, such as rotation angles and dimensional variations, on the BIC modes is systematically studied using full-wave electromagnetic simulations. The multi-mode coupling behavior is quantitatively modeled using Coupled Mode Theory (CMT), and the performance is evaluated through refractive index sensing simulations. The results indicate that the structure supports three symmetry-protected BIC modes within the 1.25–1.80 THz range, which transform into quasi-BICs under symmetry breaking. Their Q-factors increase exponentially as the asymmetry degree decreases, reaching a maximum value of 7372.75. Symmetry breaking along different directions enables independent control of specific resonance modes, exhibiting Fano lineshapes and narrowband responses. In sensing applications, the structure demonstrates high sensitivity (up to 501 GHz/RIU) and an excellent Figure of Merit (FOM = 334 RIU^-1). Notably, the proposed structure reveals the distinct control mechanism of orthogonal symmetry breaking on multi-mode coupling pathways. The constructed sensor significantly outperforms comparable devices in both sensitivity and FOM, addressing the longstanding challenge of simultaneously achieving high sensitivity and high resolution.