The stability of vegetation carbon sinks is crucial for achieving carbon neutrality and sustaining ecosystem carbon sequestration. However, existing methods for assessing carbon sink stability remain limited in their ability to capture both interannual variations and long-term trends. Here, we used Ensemble Empirical Mode Decomposition (EEMD) to separate gross primary productivity (GPP) in China's drylands (1982-2018) into interannual and trend components, and developed a framework integrating both timescales to assess overall stability and its response to aridity. Results show: (1) High interannual stability occurred in alpine grasslands and meadows of the Tibetan Plateau, desert steppes of central Inner Mongolia, and the cropland zones of the northern Loess Plateau; high trend stability was mainly on the Loess Plateau. The northern Loess Plateau exhibited high stability in both dimensions, while the dry sub-humid zone, eastern Inner Mongolia's agro-pastoral ecotone, and southern Loess Plateau showed low stability. A nonlinear relationship was observed between the two timescales, where interannual stability initially declined and then increased with increasing trend stability, with the shift occurring at a trend variance contribution of 0.24. (2) High overall stability was concentrated in alpine meadows of the Tibetan Plateau and Loess Plateau croplands, highlighting the dominant role of long-term trends. (3) Monotonic increase or decrease-to-increase trends of GPP exhibited high overall stability, with mean values of 0.66 and 0.67 respectively, whereas nonsignificant change (0.60), monotonic decrease (0.60), or increase-to-decrease (0.64) trends showed lower stability. (4) GPP stability responded nonlinearly to the Aridity Index (AI), initially declining then rising past a threshold (0.55). After thresholds were crossed, stability increased or stabilized for natural vegetation, while cropland stability declined. The aridity threshold for croplands (0.32) was lower than for forests (0.55), grasslands (0.53), and shrublands (0.55). Our findings underscore the necessity of integrating interannual and trend components to assess GPP stability.