According to the International Atomic Energy Agency’s requirements for the minimization of radioactive waste, nuclear facility components need to be cut into smaller blocks and packaged in waste containers during decommissioning. Therefore, it is important to increase the space utilization (SU) of the cut blocks in the containers while reducing the cutting time (CT). In engineering practice, increasing SU often leads to longer CTs, which poses a great challenge to improve the efficiency of the nuclear decommissioning process. To overcome this challenge and to determine the optimal operational parameters, this paper introduces a multi-objective optimization design method for cutting and packaging nuclear facility components. The goal is to increase SU while concurrently reducing CTs, ultimately minimizing the waste and reducing the decommissioning cost. First, we project the intricate three-dimensional (3D) irregular parts packing problem onto a two-dimensional plane to simplify the complexity inherent in 3D parts packing and to formulate a packing optimization model. Second, we employ the Morris method to perform global sensitivity analysis on critical parameters, including cutting angle, height, component radius, and plate thickness parameters, throughout the cutting process of nuclear facility components. This analysis produces global sensitivity indicators for each parameter, facilitating a precise assessment of the sensitivity values associated with different operational parameters. Finally, we formulate a multi-objective design optimization model for cutting and packing nuclear facility components that yields a series of alternative operating parameter solutions upon solving it. This methodology offers a resolution for the selection of optimal operational parameters in the decommissioning process of nuclear facility components, thereby attaining optimal outcomes in waste disposal and furnishing guidance for subsequent decommissioning activities.