For slowing currents, at least in the long run, there's reasonable evidence that, in the extreme, the ocean becomes anoxic[0], stops producing oxygen and starts releasing hydrogen sulfide instead. It's happened a few times in Earth's history [0] suspected to usually be caused climate change impacting ocean circulation.

Peter Ward's Under a Green Sky does a fantastic overview of this subject, and outlines how most mass extinction events have likely been triggered by sudden changes in atmospheric CO2 through various mechanism.

0. https://en.wikipedia.org/wiki/Anoxic_event