The oceanic overturning circulation has a central role in the Earth's climate system and in biogeochemical cycling, as it transports heat, carbon and nutrients around the globe and regulates their storage in the deep ocean. Mixing processes in the Antarctic Circumpolar Current are key to this circulation, because they control the rate at which water sinking at high latitudes returns to the surface in the Southern Ocean. Yet estimates of the rates of these processes and of the upwelling that they induce are poorly constrained by observations. Here we take advantage of a natural tracer-release experiment - an injection of mantle helium from hydrothermal vents into the Circumpolar Current near Drake Passage - to measure the rates of mixing and upwelling in the current's intermediate layers over a sector that spans nearly one-tenth of its circumpolar path. Dispersion of the tracer reveals rapid upwelling along density surfaces and intense mixing across density surfaces, both occurring at rates that are an order of magnitude greater than rates implicit in models of the average Southern Ocean overturning. These findings support the view that deep-water pathways along and across density surfaces intensify and intertwine as the Antarctic Circumpolar Current flows over complex ocean-floor topography, giving rise to a short circuit of the overturning circulation in these regions.