Hydroclimatic extremes are critical regulators of terrestrial carbon sink dynamics, yet their representation in terrestrial biosphere models remains highly uncertain. Here, we assessed uncertainties in Trends in Net Land-Atmosphere Exchange (TRENDY) v12 model simulations of carbon sink responses to hydroclimatic extremes during 1980-2022 by systematically comparing model outputs across regions, event types, and biomes. Site-level evaluations reveal that the multi-model ensemble mean correctly captures the sign of net biome productivity (NBP) anomalies at approximately 60% of stations; however, while the multi-model ensemble mean generally replicates NBP variations during dry events, its performance degrades during wet events. Spatially, most regions act as anomalous carbon sinks during wet extremes, a pattern that largely reverses during dry events. Despite these general trends, substantial inter-model heterogeneity persists. Inter-model uncertainties are more pronounced under dry events between 30 degrees S and 30 degrees N, while other latitudes exhibit comparable or even greater spreads under wet events. Specifically, inter-model spread is more sensitive to wet anomalies in arid and semi-arid regions, but to drought-induced stress in semi-humid and humid regions. Across biomes, uncertainties are greater for grasslands, savannas, and shrublands during wet events, shifting to forests and croplands during dry events. Finally, we demonstrate that the divergent NBP responses primarily originate from uncertainties in simulating gross primary production. Our findings highlight the persistent challenges TRENDY models face in capturing ecosystem responses to hydroclimatic extremes, underscoring the urgent need to improve simulation fidelity in a rapidly changing climate.