Dual-symmetry breakings including permittivity asymmetry and geometry asymmetry have been studied in all dielectric split-ring metamaterials supported bound states in the continuum. For any single symmetry breaking, the proposed metamaterials can support simultaneously dual quasi-bound states in the continuum (quasi-BICs). Multipolar decomposition reveals that dual quasi-BICs induced by permittivity asymmetry are both governed by magnetic dipole and electric quadrupole, whereas dual quasi-BICs induced by geometry asymmetry are governed by magnetic dipoles. Under the combined effect of the two types of symmetry breaking, it is found that the quasi-BIC can be weaken and vanished, which is different from enhanced quasi-BIC effect induced by a single symmetry breaking. In addition, asymmetric magnetic and electric field distributions can be realized by selecting different type of symmetry breaking, providing a new way of indirectly manipulating the localized magnetic fields. We show that dual-symmetry breakings point to a unique routine to analyze the physical mechanism of quasi-BICs, which furthermore provide a useful insight into their tuning behavior.