Supernova remnant (SNR) shock waves are the main place where interstellar dust grains are destroyed. However, the dust destruction efficiency in nonradiative shocks is still not well known. One way to estimate the fraction of dust destroyed is to compare the difference between postshock gas abundances and preshock medium total abundances when the preshock elemental depletion factors are known. We compare the postshock gas abundances of 16 SNRs in the Large Magellanic Cloud (LMC) with the LMC interstellar medium abundances that we derived based on 69 slow-rotating early B-type stars. We find that, on average, ∼61% of Si-rich dust grains are destroyed in the shock, while the fraction of dust destroyed is only ∼40% for Fe-rich dust grains. This result supports the idea that the high depletion of Fe in the diffuse neutral medium is not caused by the resilience of Fe-rich grains but because of faster growth rate. This work also presents a potential way to constrain the chemical composition of interstellar dust.