The geological environment of the surrounding rock in deep underground engineering will become more and more complex, along with the excavation depth continuously increasing. Under these conditions of high temperatures, high seepage, high geostress, and strong excavation disturbance, the surrounding rock during underground engineering can experience obvious nonlinear deformation failure. In order to guarantee the construction, excavation, and operational safety of deep underground engineering, we have to comprehensively study the failure characteristics and deformation characteristics of the surrounding rocks of the cavern. To reveal the interaction between structures and the characteristics of overloading-induced damage and safety factor, a geomechanical model test of an X-type cross cavern group was carried out during the excavation process and overloading process. The engineering background is the URL of HLW for the geological disposal in Beishan. This is the first time that this type of geomechanical model test is being carried out. The law of displacement and stress change during the process of excavation and the law of deformation and the failure of surrounding rock in the process of overload are obtained. The test results show that the stress and displacement changes at the intersection of the caverns are most significant after excavation. The excavation’s impact range is approximately 1.5 to 2 times the tunnel diameter. Under these test conditions, the safety coefficient of the crack initiation is 2.1, the safety coefficient of the local destruction is 2.5, and the safety coefficient of the general demolition is 2.9. These test results provide technical support for the design and construction of an URL for the deep buried geological disposal of HLW and have important practical significance.