Sparassodonta, a Metatherian monophyletic group, was the main mammalian carnivore predator clade in South America from the Paleogene to the Early Pliocene (c. 66–3.5 Ma). However, there is still no consensus on the causes of their demise. Here, we use the fossil record and Bayesian diversification models to infer the origination and extinction rates for Sparassodonta. Then, we evaluate if their demise can be attributed to global temperature changes, Andean uplift, biotic interactions with their competitor and prey clades, and body mass evolution. That is biotic aspects in the context of the Red Queen model, abiotic aspects in the context of the Court Jester model, and an intrinsic lineage attribute. Our results show that this lineage is characterized by a positive near-zero net diversification rate indicating that the clade maintained a relatively low but stable diversity until the Middle Miocene when an increase in extinction rate drove them to decline and eventual extinction. Moreover, our results support the idea that a drastic regional landscape change triggered by the Andean uplift process affected their diversification dynamics, eventually driving them to extinction. These environmental changes could explicitly affect Sparassodonta lineages due to their ever-present vulnerability to extinction by near-zero net diversification rate and their highly specialized ecology that could have constrained adaptation to new South American landscapes.