A large volume of the East Antarctic Ice Sheet drains through the Totten Glacier (TG) and is thought to be a potential source of substantial global sea level rise over the coming centuries. We show the surface velocity and height of the floating part of TG, which buttresses the grounded component, have varied substantially over two decades (1989–2011), with variations in surface height strongly anti-correlated with simulated basal melt rates (r=0.70, p<0.05). Coupled glacier/ice-shelf simulations confirm ice flow and thickness respond to both basal melting of the ice shelf and grounding on bed obstacles. We conclude the observed variability of TG is primarily ocean-driven. Ocean warming in this region will lead to enhanced ice-sheet dynamism and loss of upstream grounded ice.