We analyze the vortex core states of two-species (mass imbalanced) superfluid fermion mixtures as a function of two-body binding energy in two dimensions. In particular, we solve the Bogoliubov-de Gennes equations for a population balanced mixture of Li-6 and K-40 atoms at zero temperature. We find that the vortex core is mostly occupied by the light-mass (Li-6) fermions and that the core density of the heavy-mass (K-40) fermions is highly depleted. This is in contrast with the one-species (mass balanced) mixtures with balanced populations where an equal amount of density depletion is found at the vortex core for both pseudospin components.