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The objective of this research is to propose a novel framework for assessing the consequences of hazardous events on a water resources system using dynamic resilience. Two types of hazardous events were considered: a severe flood event and an earthquake. Given that one or both hazards have occurred and considering the intensity of those events, the main characteristics of flood dynamic resilience were evaluated. The framework utilizes an artificial neural network (ANN) to estimate dynamic resilience. The ANN was trained using a large, generated dataset that included a wide range of situations, from relatively mild hazards to severe ones. A case study was performed on the Pirot water system (Serbia). Dynamic resilience was derived from the developed system dynamics model alongside the hazardous models implemented. The most extreme hazard combination results in the robustness of 0.04, indicating a combination of an earthquake with a significant magnitude and a flood hydrograph with a low frequency of occurrence. In the case of moderate hazards, the system robustness has a median value of 0.2 and the rapidity median value of 162 h. The ANN’s efficacy was quantified using the average relative error metric which equals 2.14% and 1.77% for robustness and rapidity, respectively.