A tunable terahertz meta-resonator (TTM) is proposed to be capable of switching single- and dual-resonance characteristics in this article. The presented TTM device consists of two symmetrical E-shaped electric split-ring resonators (eSRRs) on the silicon (Si) substrate. Through the change of the gap between two eSRRs, it allows the resonances to be tuned about 78 GHz, spanning from 0.780 THz to 0.702 THz in transverse magnetic (TM) mode. When one eSRR is anchored on the Si substrate and the other suspended eSRR is heightened along the z-axis direction, the TTM device exhibits resonance-insensitive behavior in transverse electric (TE) mode, along with a convertible feature that enables it to transition between single-resonance and dual-resonance responses in TM mode. Besides, the practicality of TTM device is further enhanced by its capability to operate effectively in ambient surroundings with varying refractive indexes. In TE and TM modes, the high linearity relationship between resonances and refractive indexes is achieved with correlation coefficients both exceeding 0.99. The TTM device provides potential possibilities in tunable filters, switchable logic gates, environmental sensors, and other dynamically controllable THz-wave optoelectronics devices.