The outbreak of extraordinary disruptive events, e.g., the COVID-19 pandemic, has greatly impacted the orderly operation in global supply chains (SCs), and may lead to the SC breakdown. Regulatory actions, such as government interventions during the pandemic, can greatly mitigate the disruption propagation (i.e., the ripple effect) and improve SC viability. However, existing works that focus on the disruption propagation management have not considered the possibility of such interventions. Motivated by the fact, in this study, we investigate a new disruption propagation management problem in a multi-echelon SC with limited intervention budget. The aim is to minimize disruption risk measured by the disrupted probability of target participants in the SC. For the problem, a novel approach, combining the Causal Bayesian Network (CBN), the do-calculus and the mathematical programming, is developed. Specially, two mixed-integer non-linear programming models are constructed to determine appropriate interventions. To enhance the proposed mathematical models, two valid inequalities are proposed. Then, a problem-specific genetic algorithm (GA) is developed for handling large-scale problem instances. Numerical experiments on a case study and randomly generated instances are conducted to evaluate the efficiency of the proposed models, the valid inequalities and the GA. Based on experiment analysis, managerial insights are drawn.