Over the last 20 years, the global production of dimension stones has grown rapidly. Today, seven countries—China, India, Turkey, Iran, Italy, Brazil, and Spain—account for around two-thirds of the world's output of dimension stones. Each one has annual production levels of nine to over twenty-two million tons. Mining operation in general is one of the most hazardous fields of engineering. A large amount of dimensional stone quarries require a special scheme of risk assessment. Risk Breakdown Structure is one of the major stages of risk assessment. In this paper, a detailed structure of risks of the dimension stone quarrying is formed, and divided into 17 main levels and 128 sublevels. The complexity of identifying different parameters made it requisite to use multi-attribute decision-making methods for prioritizing associated risks. As a case study, the main risks of the Ghasre Dasht marble mine are evaluated using the VIKOR method considering 10 major parameters under a Fuzzy environment. The results showed that the economic, Management, and Schedule risks are the most threatening risks of dimensional stone quarrying.