Ocean turbulent mixing exerts an important control on the rate and structure of the overturning circulation. Recent observational evidence suggests, however, that there could be a mismatch between the observed intensity of mixing integrated over basin or global scales, and the net mixing required to sustain the overturning's deep upwelling limb. Here, we investigate the hitherto largely overlooked role of tens of thousands of seamounts in resolving this discrepancy. Dynamical theory indicates that seamounts may stir and mix deep waters by generating lee waves and topographic wake vortices. At low latitudes, this is enhanced by a layered vortex regime in the wakes. We consider three case studies (in the equatorial zone, Southern Ocean and Gulf Stream) that are predicted by theory to be representative of, respectively, a layered vortex, barotropic wake, and hybrid regimes, and corroborate theoretical scalings of mixing in each case with a realistic regional ocean model. We then apply such scalings to a global seamount dataset and an ocean climatology to show that seamount-generated mixing makes a leading-order contribution to the global upwelling of deep waters. Our work thus brings seamounts to the fore of the deep-ocean mixing problem, and urges observational, theoretical and modeling efforts toward incorporating the seamounts' mixing effects in conceptual and numerical models of the ocean circulation.