In recent years, the supply chain has undergone significant transformations due to various factors such as globalization, the COVID‐19 pandemic, advancements in information technology, outsourcing, and offshore production. These changes have made the supply network more complex, particularly with regards to sustainability issues, and have increased the vulnerability of the supply chain to sustainability‐related risks. However, despite the growing importance of sustainability‐related supply chain risks (SSCRs), there is a lack of understanding and inadequate research on critical aspects in the existing literature on this topic, such as how firms in volatile and demand‐driven sectors cope with SSCRs and how these risks affect the firms' operational performance. To address this gap, this study investigates the impact of sustainability‐related supply chain risks on suppliers, customers, and the economic performance of businesses in the garment industry in Vietnam. Using a sample of 254 garment companies, this study aims to develop a comprehensive measuring scale for supply chain sustainability risk and evaluates the effectiveness of dynamic supply chain management techniques in mitigating the impact of sustainability‐related risks on firm performance characteristics. The findings of this research reveal that there is a risk–return trade‐off for economic hazards, while no such trade‐off is observed for social and environmental hazards. Furthermore, we find that supplier management and supply chain integration methods can assist in the management of environmental hazards, leading to a positive outcome for both businesses and the environment. The research results provide both theoretical and managerial implications for mitigating the risks associated with sustainability in the supply chain. The results suggest that effective management of sustainability‐related risks can result in a win‐win scenario for both businesses and the environment.