A core concern in the research on deep geological disposal of high-level radioactive waste is the migration of radionuclides in geological bodies. Most studies on radionuclide migration consider the role of only the rock fissures without incorporating the influence of the rock matrix. In this paper, the rock mass for geological disposal of high-level radioactive waste is regarded as a fissure-pore medium. Considering the influences of radionuclide diffusion and fluid transport on radionuclide migration in the process of disposal, the governing equation of radionuclide migration and evolution in the pore-fissure medium is established. The numerical scheme of the governing equation is given based on the mixed finite volume method (FVM), using our program solution module written in C++. On this basis, the numerical test model with fissures was developed, which analyzed the radionuclide migration law in clayey rocks under various fissure and rock matrix diffusion coefficients and hydraulic conductivities. The simulation results are compared with finite element method results, revealing the superiority of the mixed FVM method in solving problems of radionuclide migration in discontinuous geological bodies containing hiatuses, mutations, and fissures. The study provides a theoretical basis for evaluating the safety, feasibility, and suitability of geological disposal repositories for high-level radioactive waste in terms of radionuclide migration.