ABSTRACT The reverse shock in the ejecta of core-collapse supernovae is potentially able to destroy newly formed dust material. In order to determine dust survival rates, we have performed a set of hydrodynamic simulations using the grid-based code astrobear in order to model a shock wave interacting with clumpy supernova ejecta. Dust motions and destruction rates were computed using our newly developed external, post-processing code paperboats, which includes gas drag, grain charging, sputtering, and grain–grain collisions. We have determined dust destruction rates for the oxygen-rich supernova remnant Cassiopeia A as a function of initial grain sizes and clump gas density. We found that up to $30\,\mathrm{{{\ \rm per\ cent}}}$ of the carbon dust mass is able to survive the passage of the reverse shock if the initial grain size distribution is narrow with radii around ∼10–50 nm for high gas densities, or with radii around $∼ 0.5\!-\!1.5\,\mathrm{\mu m}$ for low and medium gas densities. Silicate grains with initial radii around 10–30 nm show survival rates of up to $40\,\mathrm{{{\ \rm per\ cent}}}$ for medium- and high-density contrasts, while silicate material with micron-sized distributions is mostly destroyed. For both materials, the surviving dust mass is rearranged into a new size distribution that can be approximated by two components: a power-law distribution of small grains and a lognormal distribution of grains having the same size range as the initial distribution. Our results show that grain–grain collisions and sputtering are synergistic and that grain–grain collisions can play a crucial role in determining the surviving dust budget in supernova remnants.