Achieving high-Q-factor resonances allows dramatic enhancement of performance of many plasmonic devices. However, the excitation of high-Q-factor resonance, especially multiple high-Q-factor resonances, has been a big challenge in traditional metamaterials due to the ohmic and radiation losses. Here, we experimentally demonstrate simultaneous excitation of double extremely sharp resonances in a terahertz metamaterial composed of mirror-symmetric-broken double split ring resonators (MBDSRRs). In a regular mirror-arranged SRR array, only the low-Q-factor dipole resonance can be excited with the external electric field perpendicular to the SRR gap. Breaking the mirror-symmetry of the metamaterial leads to the occurrence of two distinct otherwise inaccessible ultrahigh-Q-factor modes, which consists of one trapped mode in addition to an octupolar mode. By tuning the asymmetry parameter, the Q factor of the trapped mode can be linearly modulated, while the Q factor of the octupolar mode can be tailored exponentially. For specific degree of asymmetry, our simulations revealed a significantly high Q factor (Q>100) for the octupolar mode, which is more than one order of magnitude larger than that of conventional metamaterials. The mirror-symmetry-broken metamaterial offers the advantage of enabling access to two distinct high-Q-factor resonances which could be exploited for ultrasensitive sensors, multiband filters, and slow light devices.