Between 50,000 and 3,000 years before present (BP) 65% of mammal genera weighing over 44 kg went extinct, together with a lower proportion of small mammals. Why species went extinct in such large numbers is hotly debated. One of the arguments proposes that climate changes underlie Late Quaternary extinctions, but global quantitative evidence for this hypothesis is still lacking. We test the potential role of global climate change on the extinction of mammals during the Late Quaternary. Our results suggest that continents with the highest climate footprint values, in other words, with climate changes of greater magnitudes during the Late Quaternary, witnessed more extinctions than continents with lower climate footprint values, with the exception of South America. Our results are consistent across species with different body masses, reinforcing the view that past climate changes contributed to global extinctions. Our model outputs, the climate change footprint dataset, provide a new research venue to test hypotheses about biodiversity dynamics during the Late Quaternary from the genetic to the species richness level.