A theoretical approach is proposed to describe the spin dynamics in defect color centers. The method explicitly considers 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, excited state, and an additional intermediate state. The proposed theory is applied to treat spin-dependent phenomena in silicon carbide, namely, in spin-32 silicon-vacancy centers, termed 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, 031014 (2016)10.1103/PhysRevX.6.031014].