We study the optical absorption properties of silicene and germanene in the presence of the perpendicular magnetic and electric fields. Their low-energy Landau level (LL) spectra are controllable by an external electric field, where the spin- and valley-degeneracy of the LLs are strongly influenced by the electric and Zeeman fields. The electric field has removed spin-degeneracy at a given valley. Analytical expressions for the magneto-optical absorption coefficient (MOAC) are expressed in the presence of the interaction between carriers and random impurities and the intrinsic phonons including the spin and valley effects. The results evaluated for the topological insulator and valley-spin-polarized metal phases showed that when the electric field is included, the MOAC peaks are separated for opposite spin cases where the splitting in germanene is stronger than that in silicene. The peak's intensity caused by the carrier-photon-impurity scattering is the highest, the next is the carrier-photon scattering, while the carrier-photon-phonon scattering shows the lowest in both materials. Among the different phonon modes, the out-of-plane (ZA) mode in silicene dominates the others, being attributed to its buckled atomic structure, which does not exist in graphene. When the ZA mode is taken into account, the estimated resultant mobility from the full-width at half-maximum is significantly supported by the experimental result in silicene.