We present a novel approach for managing the risks of a large complex sys- tem of systems. The methodology of system-of-systems axiomatic risk management (SoSARM) put forward here is an axiomatic-risk-based decomposition for resolving hierarchical coupled risks. The first part of the paper develops a new methodological concept to understand and quantify the relationships between higher-level and lower-level risks along with the contextual countermeasures adopted for each individual risk. In the second part of the paper, the theory and concepts developed demonstrate a typical production system of systems following a step-by-step hierarchical approach. We find the SoSARM technique to be a very simple yet comprehensive method of handling interdependent cross-domain risks.