Global warming threatens marine biota with losses of unknown severity. Here, we quantify global and local extinction risks in the ocean across a range of climate futures on the basis of the ecophysiological limits of diverse animal species and calibration against the fossil record. With accelerating greenhouse gas emissions, species losses from warming and oxygen depletion alone become comparable to current direct human impacts within a century and culminate in a mass extinction rivaling those in Earth's past. Polar species are at highest risk of extinction, but local biological richness declines more in the tropics. Reversing greenhouse gas emissions trends would diminish extinction risks by more than 70%, preserving marine biodiversity accumulated over the past ~50 million years of evolutionary history.