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 <img id="_x0000_i1026" src="../../../../img/revistas/bjp/v33n4/a13img01.gif" align=absbottom>B <img id="_x0000_i1027" src="../../../../img/revistas/bjp/v33n4/a13img01.gif" align=absbottom>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 <img id="_x0000_i1028" src="../../../../img/revistas/bjp/v33n4/a13img02.gif" align=absbottom>flux-density dependence, suggesting that the vortices mainly reduce the effective cross section over which a current of effective density j ~ j d flows.