Disasters are extraordinary shocks that disrupt every aspect of the community life. Lives are lost, infrastructure is destroyed, the social fabric is torn apart, and people are left with physical and psychological trauma. In the aftermath of a disaster, communities begin the collective process of healing, grieving losses, repairing damage, and adapting to a new reality. Previous work has suggested the existence of a series of prototypical stages through which such community responses evolve. As social media have become more widely used, affected communities have increasingly adopted them to express, navigate, and build their response due to the greater visibility and speed of interaction that these platforms afford. In this study, we ask if the behavior of disaster-struck communities on social media follows prototypicalpatterns and what relationship, if any, these patterns may have with those established for offline behavior in previous work. Building on theoretical models of disaster response, we investigate whether, in the short term, community responses on social media in the aftermath of disasters follow a prototypical trajectory. We conduct our analysis using computational methods to model over 200 disaster-stricken U.S. communities. Community responses are measured in a range of domains, including psychological, social, and sense-making, and as multidimensional time series derived from the linguistic markers in tweets from those communities. We find that community responses on Twitter demonstrate similar response patterns across numerous social, aspirational, and physical dynamics. Additionally, through cluster analysis, we demonstrate that a minority of communities are characterized by more intense and enduring emotional coping strategies and sense-making. In this investigation of the relationship between community response and intrinsic properties of disasters, we reveal that the severity of the impact makes the deviant trajectory more likely, while the type and duration of a disaster are not associated with it.