Cyclones cause major damage to mangrove ecosystems globally. While this damage is projected to increase as storms intensify with climate change, the consequences of changes in cyclone attributes other than wind speed remain largely unexplored. Here, we show that shifts in cyclone travel speed may also dramatically alter the risks and mechanisms of damage. By developing an interpretable machine learning model trained with all cyclones recorded worldwide from 2001 to 2021, we find that fast-moving cyclones tend to be especially destructive on steeply sloping coasts, exacerbating physical damage, whereas slow-moving cyclones induce predominantly hydrological damage. Between 1981-2000 and 2001-2020, exposure of global mangrove ecosystems to cyclones increased by 13%, accompanied by substantial changes in cyclone travel speeds, with exposure to slow- and fast-moving cyclones doubling in, respectively, the Caribbean and East Asia. Our results highlight opportunities to integrate regional shifts in cyclone attributes under a changing climate into mangrove management strategies.