Multi-mode dynamics with Zitterbewegung of an electron in 2D Dirac crystal placed in the field of monochromatic radiation is studied. For calculations, a model Hamiltonian taking into account two independent Dirac points has been used. Calculations have shown that the spectrum of electron oscillations contains a series of new (compared to the usual Zitterbewegung) frequencies. The latter, in the case of a high radiation frequency, are a combination of the Zitterbewegung frequency and frequencies that are multiples of the field frequency. In the case when the field frequency is comparable to the Zitterbewegung frequency, the spectrum of electron oscillations is determined by the field amplitude. The character of this dependence has been shown to be changed by variation of the direction of radiation polarization. The possibility of the appearance of a constant component of the electron velocity in the field of monochromatic radiation is also discussed.