Quantifying the efficiency of dust destruction in the interstellar medium (ISM) due to supernovae (SNe) is crucial for the understanding of galactic dust evolution. We present 3D hydrodynamic simulations of an SN blast wave propagating through the ISM. The interaction between the forward shock of the remnant and the surrounding ISM leads to destruction of ISM dust by the shock-heated gas. We consider the dust processing due to ion sputtering, accretion of atoms/molecules, and grain-grain collisions. Using 2D slices from the simulation time series, we apply post-processing calculations using the PAPERBOATS code. We find that efficiency of dust destruction depends strongly on the rate of grain shattering due to grain-grain collisions. The effective dust destruction is similar to previous theoretical estimates when grain-grain collisions are omitted, but with grain shattering included, the net destruction efficiency is roughly one order of magnitude higher. This result indicates that the dust-destruction rate in the ISM may have been severely underestimated in previous work, which only exacerbates the dust-budget crises seen in galaxies at high redshifts.