A numerical model is presented to predict the time-resolved evolution of the spatial intensity distribution of the laser pulses in the super-Gaussian mirror resonator, taking into account diffraction and stored energy depletion. The beam-quality factor M2 is calculated during the pulse evolution. Simulation results show that gain saturation affects the beam quality of the Q-switched solid-state lasers, the corresponding values of the M2 parameter increase during the pulse evolution. The spatial distribution of laser pulse first starts on the resonator axis with a Gaussian-shaped spot, then expands very quickly and forms a donut-shaped profile towards the end of the pulse.