The total ionizing dose (TID) effect of amorphous Indium–Gallium–Zinc Oxide (a-IGZO) thin film transistors (TFT) was investigated in four bias modes. The degradation mechanism induced by TID in various bias modes was analyzed using technology computer-aided design (TCAD) tools. The findings revealed that, in the negative bias mode, the strongest electric field affects the probability of holes in the SiO2 passivation layer and SiO2 buffer layer being trapped by interface traps, while also increasing the radiation charge generation rate. Consequently, this led to the most significant degradation in device performance. To alleviate the impact of TID effect on the performance of back-gated a-IGZO TFT, it is necessary to appropriately reduce the thickness of SiO2 buffer layer and consider alternative passivation layer materials. This will decrease the volume of electron–hole pairs in the dielectric layer under irradiation and minimize the likelihood of the trapping by interface traps. These results lay the groundwork for promoting the application of a-IGZO TFT in space radiation environments.