A simplified neutrosophic set is characterized by a truth-membership function, an indeterminacy-membership function, and a falsity-membership function, which is a subclass of the neutrosophic set and contains the concepts of an interval neutrosophic set and a single valued neutrosophic set. It is a powerful structure in expressing indeterminate and inconsistent information. However, there has only been one paper until now—to the best of my knowledge—on the subtraction and division operators in the basic operational laws of neutrosophic single-valued numbers defined in existing literature. Therefore, this paper proposes subtraction operation and division operation for simplified neutrosophic sets, including single valued neutrosophic sets and interval neutrosophic sets respectively, under some constrained conditions to form the integral theoretical framework of simplified neutrosophic sets. In addition, we give numerical examples to illustrate the defined operations. The subtraction and division operations are very important in many practical applications, such as decision making and image processing.