  We perform radiation hydrodynamics simulations to study the structure and
evolution of a photoevaporating protoplanetary disk. Ultraviolet and X-ray
radiation from the host star heats the disk surface, where H$_2$ pumping also
operates efficiently. We run a set of simulations with varying the amount of
dust grains, or the dust-to-gas mass ratio, which determines the relative
importance between photoelectric heating and H$_2$ pumping. We show that H$_2$
pumping and X-ray heating contribute stronger to the mass-loss of the disk if
the dust-to-gas mass ratio is $\mathcal{D}\leq10^{-3}$.The disk mass loss rate
decreases with a lower dust amount, but remains around $10^{-10-11} M_{\odot}
{\rm yr}^{-1}$. In such dust-deficient disks, H$_2$ pumping enhances
photoevaporation from the inner disk region and shapes the disk mass-loss
profile. We thus argue that the late-stage disk evolution is affected by the
ultra-violet H$_2$ pumping effect. The mass-loss rates derived from our
simulations can be used in the study of long-term disk evolution.
