The Southern Ocean (SO) connects major ocean basins and hosts large air-sea carbon fluxes due to the resurfacing of deep nutrient and carbon rich waters, driven by strong surface winds. Vertical mixing in the SO, induced by breaking waves excited by strong surface winds and interaction of tides, jets and eddies with rough topography, has been considered of secondary importance for the global meridional overturning circulation. Its importance for biological cycles has largely been assumed to be due to the role of mixing in changing the underlying dynamics on a centennial timescale. Using an eddy-resolving ocean model that assimilates an extensive array of observations, we show that altered mixing can cause up to a 40\% change in SO air-sea fluxes in only a few years through altering the distribution of dissolved inorganic carbon, alkalinity, temperature and salinity. Such enhanced mixing may be induced by the propagation of tidal waves from around the globe to the SO as well as the flux of wave energy from the deep SO to shallow depths. Such processes are unresolved in climate models, yet essential.