Droughts are expected to become more frequent and severe, due to climate change, with uncertain consequences for savanna vegetation. Drought-driven tree mortality has been observed in some savannas, but little is known about how tolerant savanna trees are to drought, or what determines differences among species in drought vulnerability. Here, we examine which characteristics best distinguished tree species that were most negatively affected by a recent drought in Kruger National Park, South Africa. Woody-encroaching, root-suckering species, which tended to have relatively low investments in non-structural carbohydrates, had the highest mortality rates. Of particular interest was Dichrostachys cinerea, a notable contributor to widespread woody encroachment across southern African savannas, which suffered high drought mortality. Using rainfall maps and vegetation survey data, we show that D. cinerea distributions in Kruger National Park are limited to areas with higher mean annual rainfall and lower past drought frequency, and stem densities are lower where droughts have occurred more frequently, suggesting that past droughts have had lasting impacts on the distribution and abundance of this species. Woody encroachers, such as D. cinerea, may face a trade off between traits promoting proliferation vs. drought tolerance, and more frequent and severe droughts could increasingly limit their spread.