Human activities and climate change have accelerated species losses and degradation of ecosystems to unprecedented levels. Both theoretical and empirical evidence suggest that extinction cascades contribute substantially to global species loss. The effects of extinction cascades can ripple across levels of ecological organization, causing not only the secondary loss of taxonomic diversity but also functional diversity erosion. Here, we take a step forward in coextinction analysis by estimating the functional robustness of reef fish communities to species loss. We built a tripartite network with nodes and links based on a model output predicting reef fish occupancy (113 species) as a function of coral and turf algae cover in Southwestern Atlantic reefs. This network comprised coral species, coral‐associated fish (site occupancy directly related to coral cover), and co‐occurring fish (occupancy indirectly related to coral cover). We used attack‐tolerance curves and estimated network robustness ( R ) to quantify the cascading loss of reef fish taxonomic and functional diversity along three scenarios of coral species loss: degree centrality (removing first corals with more coral‐associated fish), bleaching vulnerability and post‐bleaching mortality (most vulnerable removed first), and random removal. Degree centrality produced the greatest losses (lowest R ) in comparison with other scenarios. In this scenario, while functional diversity was robust to the direct loss of coral‐associated fish ( R = 0.85), the taxonomic diversity was not robust to coral loss ( R = 0.54). Both taxonomic and functional diversity showed low robustness to indirect fish extinctions ( R = 0.31 and R = 0.57, respectively). Projections of 100% coral species loss caused a reduction of 69% of the regional trait space area. The effects of coral loss in Southwestern Atlantic reefs went beyond the direct coral‐fish relationships. Ever‐growing human impacts on reef ecosystems can cause extinction cascades with detrimental consequences for fish assemblages that benefit from corals.Read less <