It has been shown that the generation of the 1st Stokes component (λ = 1.538 μm) in an Nd:KGW laser with a passive V:YAG Q-switch is multimodal and its dynamics have a complex spatio-temporal character. The SRS-generation features the impact excitation manifested as the formation of a high-intensity peak at the beginning of the pulse, the peak position relative to the subsequent part of the pulse depending on the radius of curvature of the end cavity mirror. The SRS-conversion of the fundamental laser radiation (λ = 1.351 μm) starts in the central region of the Nd:KGW-element and then spreads towards its boundaries. The total integral SRS-pulse of duration 15-25 ns represents an envelope of shorter (1-2 ns) time-shifted pulses generated by separate local areas of the active medium cross-section. The multimode character of generation results in gradual damage to the V:YAG Q-switch at the attained SRS-radiation energy of 8-14 mJ.