Mounting evidence suggests that climate change will cause shifts of tree species range and abundance (biomass). Abundance changes under climate change are likely to occur prior to a detectable range shift. Disturbances are expected to directly affect tree species abundance and composition, and could profoundly influence tree species spatial distribution within a geographical region. However, how multiple disturbance regimes will interact with changing climate to alter the spatial distribution of species abundance remains unclear. We simulated such forest demographic processes using a forest landscape succession and disturbance model (LANDIS‐II) parameterized with forest inventory data in the northeastern United States. Our study incorporated climate change under a high‐emission future and disturbance regimes varying with gradients of intensities and spatial extents. The results suggest that disturbances catalyze changes in tree species abundance and composition under a changing climate, but the effects of disturbances differ by intensity and extent. Moderate disturbances and large extent disturbances have limited effects, while high‐intensity disturbances accelerate changes by removing cohorts of mid‐ and late‐successional species, creating opportunities for early‐successional species. High‐intensity disturbances result in the northern movement of early‐successional species and the southern movement of late‐successional species abundances. Our study is among the first to systematically investigate how disturbance extent and intensity interact to determine the spatial distribution of changes in species abundance and forest composition.