This article mainly investigated the incident and exit surfaces of terbium gallium garnet (TGG) magneto-optical elements by damaged by the laser with wavelength of 1064 nm through pump-probe imaging technology. The damage characteristics of terbium gallium garnet elements under fundamental 1064 nm pulsed laser irradiation were studied. The results indicated that the coated TGG element exhibited a lower damage threshold at the incident surface compared with the exit surface, and the difference in damage morphology between the entrance and exit surface was mainly influenced by laser-induced plasma effects. It was found that the initial damage on the TGG incident surface mainly came from impurities and defects in the coatings, and the separation of the film layer under high energy would occur; The exit surface damage of coated TGG components was mainly induced by impurity defects in the substrate material, and the size of damage pits increased gradually under higher laser energy. By analyzing the influence of factors such as laser pulse energy, plasma effect, and material damage response on the laser damage threshold, this study provided important and reference for improving the anti-damage ability of TGG magneto-optical materials under high-power laser irradiation.