The electromagnetically induced transparency effect of terahertz metamaterials exhibits excellent modulation and sensing properties, and it is critical to investigate the modulation effect of the transparent window by optimizing structural parameters. In this work, a unilateral symmetrical metamaterial structure based on the cut-wire resonator and the U-shaped split ring resonator is demonstrated to achieve electromagnetically induced transparency-like (EIT-like) effect. Based on the symmetrical structure, by changing the structural parameters of the split ring, an asymmetric structure metamaterial is also studied to obtain better tuning and sensing characteristics. The parameters for controlling the transparent window of the metamaterial are investigated in both passive and active modulation modes. In addition, the metamaterial structure based on the cut-wire resonator, unilateral symmetric and asymmetric configurations are investigated for high performance refractive index sensing purposes, and it is found that the first two metamaterial structures can achieve sensitivity responses of 63.6 GHz/RIU and 84.4 GHz/RIU, respectively, while the asymmetric metamaterial is up to 102.3 GHz/RIU. The high sensitivity frequency response of the proposed metamaterial structures makes them good candidates for various chemical and biomedical sensing applications.