Frequent droughts threaten terrestrial carbon sequestration by altering stomatal conductance and canopy structure; however, the mechanisms underlying the drought response and their drivers in northern China's grasslands remain unclear. In this study, bivariate copula models were used to estimate response times, loss probabilities, and drought trigger thresholds for the normalized difference vegetation index (NDVI) and gross primary productivity (GPP) across grassland types and the background drought gradient, and XGBoost-SHAP was applied to identify key drivers and interactions underlying threshold variability. The results show that drought impacts peak during June-August, characterized by the shortest response times, highest loss probabilities, and lowest trigger thresholds. Compared with the NDVI, GPP generally responds faster to drought. Inner Mongolia experiences the greatest losses under extreme drought on a spatial basis. The alpine meadow and alpine steppe areas present the lowest drought trigger thresholds, indicating that these areas are more vulnerable than other grassland types. In alpine steppe and temperate meadow, GPP loss is triggered by weaker drought than NDVI loss, whereas the opposite pattern is observed in meadow steppe, desert steppe, and alpine meadow. Along the mean annual standardized precipitation-evapotranspiration index (SPEI) gradient, loss probabilities increase linearly under mild and moderate drought but respond nonlinearly under severe and extreme drought, whereas the trigger thresholds of the two metrics increase linearly and intersect at SPEI = 0.67. GPP is more vulnerable in drier regions, whereas NDVI is more vulnerable in wetter regions. Shortwave radiation dominated both trigger thresholds. Precipitation contributes more strongly to NDVI responses, whereas vapor pressure deficit is more influential on GPP responses. These results clarify grassland drought response mechanisms and provide a quantitative basis for drought risk management.