Sulfuric acid leaching of copper anode slime (CAS) in the presence of manganese(IV) oxide (MnO2) and graphite was investigated for Se, Te and Ag recovery. The study reveals that the leaching of Se, Te and Ag was facilitated by the galvanic interaction with MnO2, and graphite played the role of a catalyst. The leaching process could yield 81.9% Se, 90.8% Te, and 80.7% Ag leaching efficiency when the conditions were maintained as 500 rpm, 2.0 M H2SO4, 0.8/0.8/1 MnO2/graphite/CAS, and 90 °C temperature. The kinetic study showed that Se leaching followed the surface chemical reaction at all the tested temperature range (25–90 °C) with the activation energy of 27.7 kJ/mol. Te and Ag leaching at temperature 25–50 °C followed the mixed and surface chemical reaction models, respectively, and changed to fit the diffusion and mixed control models, respectively, in the temperature range 60–90 °C with the corresponding activation energy of 17.8 and 12.2 kJ/mol.