After the excavation of an underground cavern, how the surrounding rock and the support work together to bear the excavation load is an important prerequisite to correctly analyze the joint force characteristics; effectively play the role of support; and ensure the safety, efficiency, and economy of underground cavern construction. Starting from the elastic-plastic load release characteristics of surrounding rock, this paper proposes a calculation method of the elastic load coefficient of surrounding rock and a graded release method of plastic load, which ensures the actual effect of the synergistic action of the first support and surrounding rock. Based on the elastic-plastic damage evolution characteristics of surrounding rock, a weighted iterative calculation method of elastic-plastic damage is proposed, and an evaluation method of load release ultimate bearing capacity of surrounding rock is determined. By monitoring the change law of rock acoustic wave velocity with surrounding rock damage, the relationship between the wave velocity and the damage coefficient of the surrounding rock in the excavation process is deduced, and it is proposed to determine the latest support time for first support by using the measured rock damage wave velocity. Through the numerical simulation analysis of a diversion tunnel excavation and support, the damage evolution law of the surrounding rock with the release of the excavation load is studied. The ultimate bearing capacity of various surrounding rocks and supporting opportunity is determined. The results demonstrate the validity and practicality of the analysis and calculation methods in this paper, which provide a new idea and analysis method for quantifying the bearing capacity of surrounding rock and determining the support timing in the excavation and support design of underground caverns.