Background subsurface vertical mixing rates in the Southern Ocean (SO) are known to vary by an order of magnitude temporally and spatially, due to variability in their generating mechanisms, which include winds and shear instabilities at the surface, and the interaction of tides and lee waves with rough bottom topography. There is great uncertainty in the parameterisation of this mixing in coarse resolution Earth System Models (ESM), and in the impact that this has on SO biological productivity on sub decadal timescales. Using a data assimilating biogeochemical-ocean model we show that SO phytoplankton productivity is highly sensitive to altering the background diapycnal mixing over short timescales. Changes the background vertical mixing rates alter key biogeochemical and physical conditions. A combination of reduced nutrient limitation and reduced light limitation causes a strong increase in SO phytoplankton productivity with higher background mixing. This leads to increased carbon export, which could alter the strength of the SO biological carbon pump and atmospheric CO$_2$ concentration over longer timescales, demonstrating the importance of an accurate representation of diapycnal mixing in ESM.