Most species disappear by the processes of background extinction, yet those processes are poorly understood. We analyzed the evolutionary dynamics of 19 Cenozoic terrestrial mammalian clades with rich fossil records that are now fully extinct or in diversity decline. We find their diversity loss was not just a consequence of "gamblers ruin" but resulted from the evolutionary loss to the Red Queen, a failure to keep pace with a deteriorating environment. Diversity loss is driven equally by both depressed origination rates and elevated extinction rates. Although we find diversity-dependent origination and extinction rates, the diversity of each clade only transiently equaled the implied equilibrium diversity. Thus, the processes that drove diversity loss in terrestrial mammal clades were fundamentally nonequilibrial and overwhelmed diversity-dependent processes.