Leaching of constituent metals from copper anode slime/CAS (22.23% Se, 1.53% Te, 9.66% Ag) by sulfuric acid in the presence of manganese(IV) oxide (MnO₂) and graphite has been investigated at a range conditions by varying stirring speed (200–600 rpm), H₂SO₄ concentration (0.5–3.0 M), MnO2/CAS and graphite/CAS mass ratio (0–1/1) and temperature (25–90 °C). The metal leaching was facilitated by the galvanic interaction with MnO₂, while graphite play role as a catalyst. Under the most suitable conditions (500 rpm, 2.0 M H₂SO₄, 0.8/0.8/1 MnO₂/graphite/CAS mass ratio and 90 °C temperature), the extent of leaching of Se, Te and Ag from the CAS, together with Mn from MnO₂ after 6 h was 90.8%, 81.9%, 80.7% and 84.1%, respectively, as compared to 76.8% Te, 69.4% Se, 67.2% Ag and 55.9% Mn after leaching of CAS with MnO₂ without graphite under the similar conditions, and against still lower leaching in the absence of MnO₂ (32.6% Te and negligible Se and Ag). The leaching results (CAS+MnO₂+graphite) of tellurium and silver at temperature 25–50 °C well fitted to the mixed and surface chemical reaction models, respectively, and changed to follow the diffusion and mixed control models in the temperature range 60–90 °C with the respective apparent activation energies of 17.8 and 12.2 kJ/mol. That of selenium was controlled by the surface chemical reaction with the estimated activation energy of 27.6 kJ/mol in the temperature range 25–90 °C. And manganese leaching followed the mixed-control model (activation energy of 56.7 kJ/mol) at the all tested temperature.