Compound disasters are highly complex and can involve different types of disasters. Since the beginning of the COVID-19 pandemic, compound disasters of public health emergencies, accident disasters, and natural hazards have occurred frequently all over the world; therefore, it is important to establish effective compound disaster emergency collaboration networks. Thus, this study examined the 7 March building collapse in Quanzhou City as a case study. This case was a typical compound disaster involving a public health emergency and an accident disaster during COVID-19. Based on the network analysis, the overall response and dynamic characteristics of the emergency collaboration for compound disasters were examined in this study. A compound disaster emergency collaboration network (ECN) was constructed by identifying the interactional relationships between emergency organizations. After applying time slices, the dynamic evolution of network structure, organizational–functional relations, organizational attributes, and cross-organizational relationships were discussed. The research results showed the following: (1) The density and connectivity of the compound disaster ECN first decreased before increasing. Meanwhile, the evolution of the network structure followed a path from decentralized to concentrated and from being uneven to an equilibrium. (2) The characteristics and practices of compound disasters during different periods indicated varied emergency needs for emergency organizations. We found that the formation of emergency tasks not only involved the passive adaptation to match the practice for compound disasters, but also the active choices of emergency organizations when facing compound disasters according to their collective experiences and decisions. (3) The national emergency management departments, the government emergency rescue organizations, and the local governments were the core organizations of the ECN. Public health management departments and social organizations were also required to participate in the ECN to improve the diverse and heterogeneous distribution of resources. (4) With increased demands during a compound disaster emergency, the number of cross-organizational collaborative relationships gradually increased. This study explored compound disaster emergencies from the perspective of network analysis to improve our understanding of the current and developing organizational relationships and practices during a compound disaster event. The dynamic characteristics of compound disasters require efficient adaptation and improvements of the collaborative mechanisms involved during emergencies.