Situated at the core of the Asian arid zone, the Tarim River Basin (TRB) serves as a critical indicator of regional hydroclimatic responses to global warming. Utilizing 27 extreme climate indices recommended by the Expert Team on Climate Change Detection and Indices, this study analyzes the spatiotemporal evolution of climate extremes in the TRB from 1960 to 2022 and explores their correlations with primary large-scale atmospheric circulation factors. The results indicate that, at the temporal scale, extreme warm indices (TX90P, TN90P, SU25, TR20) and most extreme precipitation indices (except for CDD) exhibited increasing trends, accompanied by pronounced abrupt changes and periodic characteristics. The changes were characterized by stronger warming at low temperatures than at high temperatures, greater nighttime warming than daytime warming, and larger increases in warm days than cold days. Extreme temperature and precipitation indices underwent abrupt changes in the mid-to-late 1990s and 1980s, respectively. The former exhibits pronounced "cold-warm" oscillations at 10-15-year and 25-35-year scales, while the latter displays distinct "wet-dry" cyclic alternations at 8-9-year and 30-32-year scales. Spatially, extreme temperature indices showed consistent warming across most stations. In contrast, the change trends of extreme precipitation indices displayed obvious spatial heterogeneity, with growth rates generally decreasing from west to east. Further analyses demonstrate that most extreme climate indices exhibit significant linear correlations with the AMO, PDO, NAO, and NOI. Notably, the AMO emerges as the dominant driver of variations in both extreme temperature and precipitation. In the context of accelerated global warming, these insights are pivotal for enhancing regional climate risk management and water resource adaptability.