We have investigated the low-temperature (T < Tc=10) mixed-state current-voltage (IV) response of magnesium diboride films beyond the point where the superconductivity is completely destroyed and the system enters the normal state. The resistance-versus-current R(I) curves are extremely steep and featureless, with a critical current density j c, marking the onset of dissipation, that is unusually high (j c>j d/10) with respect to the depairing current density j d. At large flux densities Hc2/10 $\lessim$ B $\lessim$Hc2, the R(I) curve has a functional shape that is largely independent of B, indicating that the rise in resistivity with increasing current occurs mainly due to pair-breaking rather than flux motion. The macroscopic destruction current I*, which drives the system normal, has a B/Hc2: $\sqrt{B/H_{c2}}$ flux-density dependence, suggesting that the vortices mainly reduce the effective cross section over which a current of effective density j ~ j d flows.
