Supply chain managers consistently face the conundrum of battling the severe and unpredictable impacts of Black Swan events in recent decades. These disruptions highlight the limitations of traditional risk management approaches, which often fail to address the fat-tail risks inherent in complex systems. This study provides actionable insights to help supply chain managers manage disruptions from Black Swan events by adopting a Complexity Science perspective. By analysing the dynamics of fat-tail risks in multi-echelon Global Supply Chain Network, this research offers a foundational understanding of how these networks behave under extreme conditions. Simulation results reveal that the frequency and magnitude of disruptions follow a power-law distribution, signifying their scale-invariance and universal nature properties also observed in other complex systems, such as earthquakes and financial markets. Building on this foundation, the study derives the scaling exponent, enabling the determination of Expected Maximum Risk over future time horizons. The scaling exponent is validated through a case study using real-world data on global bankruptcies during the COVID-19 pandemic, demonstrating its practical utility in projecting worst-case disruptions. Additionally, a conceptual Vulnerability Index is introduced, guiding supply chain managers in identifying and prioritizing critical nodes within the network for targeted risk mitigation. By bridging theoretical insights with practical applications, this study presents supply chain managers with an actional insight to mitigate the severe impacts of Black Swan events.