Non-native species can alter patterns of species diversity at multiple spatial scales, but the processes that underlie multi-scale effects remain unclear. Here we show that non-native species reduce native diversity at multiple scales through simultaneous disruption of two processes of native community assembly: species immigration, which enhances alpha diversity, and community divergence, which enhances beta diversity. Community divergence refers to the process in which local communities diverge over time in species composition because the history of species immigration and, consequently, the way species affect one another within communities are variable among communities. Continuous experimental removal of species over four years of floodplain succession revealed that, when non-native species were excluded, stochastic variation in the timing of a dominant native species' arrival allowed local communities to diverge, thereby enhancing beta diversity, without compromising promotion of alpha diversity by species immigration. In contrast, when non-native species were allowed to enter experimental plots, they not only reduced native alpha diversity by limiting immigration, but also diminished the dominant native species' role in enhancing native beta diversity. Our results highlight the importance of community assembly and succession for understanding multi-scale effects of non-native species.