Extreme weather induced by climate change can have major consequences for human health. In this study, I quantify the effect of tropical storm frequency and severity on mortality using objective meteorological data and the universe of vital statistics records from a large developing country, Mexico. Using a measure of storm exposure that accounts for both windspeed dispersion and population density along the storm track, I project changes in past storm-related mortality under various scenarios of continued climate change, while holding population and income at current levels. I find that storm-related deaths would have risen under most climate change scenarios considered, with increases of as much as 52% or declines of as much as 10%, depending on the interplay between increasing storm severity and decreased frequency.