The transport properties of an artificial single-molecule magnet based on a CdTe quantum dot doped with a single Mn +2 ion (S = 5/2) are investigated by the non-equilibrium Green function method. We consider a minimal model where the Mn-hole exchange coupling is strongly anisotropic so that spin-flip is suppressed and the impurity spin S and a hole spin s entering the quantum dot are coupled into spin pair states with (2S + 1) sublevels. In the sequential tunneling regime, the differential conductance exhibits (2S + 1) possible peaks, corresponding to resonance tunneling via (2S + 1) sublevels. At low temperature, Kondo physics dominates transport and (2S + 1) Kondo peaks occur in the local density of states and conductance. These peaks originate from the spin-singlet state formed by the holes in the leads and on the dot via higher-order processes and are related to the parallel and antiparallel spin pair states.