A theoretical approach is proposed to treat the spin dynamics in defect color centers. The method explicitly takes into account the spin dynamics in the ground state and excited state of the defect center as well as spin state dependent transitions involving the ground state and excited state, as well as an additional intermediate state. The proposed theory is applied to treat spin-dependent phenomena is silicon carbide, namely, in spinsilicon-vacancy centers, VSi or V2 centers. Theoretical predictions of magnetic field dependent photoluminescence intensity and optically detected magnetic resonance spectra demonstrate an important role of level crossing phenomena in the spin dynamics of the ground state and excited state. The results are in good agreement with previously published experimental data [Phys. Rev. X, 6 (2016) 031014].