Based on the increasing trend in drought hazards and the current drought risk assessments limited within a static spatial dimension, this study takes the Sichuan Basin (SB), a large agricultural planting area in southwestern China, as the study area and develops a comprehensive drought risk assessment. This assessment includes five components—hazard, exposure, vulnerability, mitigation capability and resilience—in three dimensions, i.e., the static dimension of space (SDS), the dynamic dimension of time (DDT), and the coupled dimension of space and time (CDTS), and this study uses the random forest algorithm to determine the weight coefficients for 18 factors in the drought assessment system. The results show that (1) there is obvious spatial heterogeneity between the drought risk in the SDS and that in the DDT, the centroid of each drought risk level in the CDTS is closer to that in the SDS. (2) The drought risk in the SDS in the SB is primarily determined by the precipitation, cultivated land ratio, and temperature, while that in the DDT is mainly affected by the trends in precipitation and gross domestic product (GDP). (3) The regions with a high level of drought risk in the SDS are mainly located in the central SB, owing to low precipitation, a high ratio of cultivated land, and low vegetation coverage. The regions with a high level of drought risk in the DDT are concentrated in the northeastern SB due to the weak increasing trends in precipitation and GDP. The necessity and scientific nature of the drought assessment in the CDTS proposed in this study are demonstrated.