The metasurfaces (MSs) can trap incoming photons at sub-wavelength scales that enable complex wavefront control including frequency, dispersion, polarization, amplitude, orbital angular and spin angular momentum. Photonic bound states in the continuum (BICs) are non-radiative solutions of the wave equation in an open system whose frequency is embedded in the continuum spectrum, thus manifesting as ultrahigh Q factor resonances. In this work, we propose a fourfold rotationally symmetric (C4v) all-dielectric THz-MS consist of a free-standing periodic array of cylindrical resonators. Empowered point group theory, we analyze the C4v characteristics of the designed THz-MS and demonstrate that it can support two symmetry-protected BICs (SP-BICs) with topological charge ± 1 at the center of momentum space. After breaking the in-plane symmetry of the metasurface, original perfect BICs transform into spectrally observable quasi-BICs with ultrahigh Q factor and ultra-narrow resonance linewidth that obey the inverse-square law. A multipole decomposition analysis indicates that one of the modes is associated with a rare electronic toroidal dipole resonance, while the other is dominated by a magnetic dipole. The dual symmetry-broken quasi-BICs terahertz metasurface offers a promising scheme toward achieving ultrahigh-Q BICs resonances and may find exciting applications in boosting light-matter interactions.