We characterize experimentally the dynamics of the electro-opto-mechanical effect (macroscopic deformation with electro-optical effect) in monodomain liquid crystal elastomers swollen by low molecular mass liquid crystals. The optical and mechanical rise times (in response to field-on) decrease in almost proportion to the square of field strength, while the corresponding decay times (in response to field-off) are nearly independent of field strength. The optical rise and decay times are about 1 order of magnitude smaller than the mechanical ones. We propose a simple model to capture the main features of both static and dynamic aspects of the electro-opto-mechanical effect and use it to interpret the experimental data.