Around 34 Mya, the Eocene-Oligocene transition (EOT) marked the most dramatic global climatic cooling of the Cenozoic. On a planetary scale, paleontological evidence suggests that this transition was associated with major faunal turnovers, sometimes even regarded as a mass extinction crisis. In South America, there is no consensus on the response of the endemic mammals to this transition. Here, using a vetted fossil dataset and cutting-edge Bayesian methods, we analyzed the dynamics of South American mammal (SAM) diversification and their possible drivers across latitude (tropical vs. extratropical), taxonomic groups, and trophic guilds throughout the Eocene-Oligocene ( 56 to 23 Ma). Our results did not evidence any mass extinction among SAM at the EOT. Instead, they experienced a gradual and long-term diversity decline from the middle Eocene to the early Oligocene, followed by a sudden waxing-and-waning diversity associated with a large taxonomic-but not ecological-turnover. Tropical and extratropical lineages have had very distinct macroevolutionary histories. No effective change in the pace at which tropical lineages diversify was found, thus favoring the tropical stability hypothesis proposed by Wallace. Diversity-dependent effects, temperature, and Andean uplift were recovered as probable drivers of SAM diversification across the period. Contrasting evidence casts doubt on the common hypothesis primarily linking Oligocene faunal changes to grassland expansion. Our findings illustrate the uniqueness of the deep-time interplay between endemic SAM and their physical environment in a context of climatic shift, highlighting the need to consider regional idiosyncrasies for understanding the coevolution of life and climate.