We demonstrate that superclean d-wave superconductors display a novel type of vortex dynamics: At low temperatures, both dissipative and transverse components of the flux-flow conductivity are found to approach universal values independent of relaxation. A finite dissipation in the superclean limit is explained in terms of the Landau damping on zero-frequency vortex modes which appear due to minigap nodes in the bound-state spectrum in the vortex core.