We present the analysis of supernova remnants ( SNRs ) in the Large Magellanic Cloud ( LMC ) and their influence on the environment at far-infrared ( FIR ) and submillimeter wavelengths . We use new observations obtained with the Herschel Space Observatory and archival data obtained with the Spitzer Space Telescope , to make the first FIR atlas of these objects . The SNRs are not clearly discernible at FIR wavelengths , however their influence becomes apparent in maps of dust mass and dust temperature , which we constructed by fitting a modified black-body to the observed spectral energy distribution in each sightline . Most of the dust that is seen is pre-existing interstellar dust in which SNRs leave imprints . The temperature maps clearly reveal SNRs heating surrounding dust , while the mass maps indicate the removal of 3.7 ^ { +7.5 } _ { -2.5 } M _ { \odot } of dust per SNR . This agrees with the calculations by others that significant amounts of dust are sputtered by SNRs . Under the assumption that dust is sputtered and not merely pushed away , we estimate a dust destruction rate in the LMC of 0.037 ^ { +0.075 } _ { -0.025 } M _ { \odot } yr ^ { -1 } due to SNRs , yielding an average lifetime for interstellar dust of 2 ^ { +4.0 } _ { -1.3 } \times 10 ^ { 7 } yr. We conclude that sputtering of dust by SNRs may be an important ingredient in models of galactic evolution , that supernovae may destroy more dust than they produce , and that they therefore may not be net producers of long lived dust in galaxies .