From integral field data we extract the optical spectra of 20 shocked clouds in the supernova remnant N132D in the Large Magellanic Cloud (LMC). Using self-consistent shock modeling, we derive the shock velocity, pre-shock cloud density, and shock ram pressure in these clouds. We show that the [Fe X] and [Fe XIV] emission arises in faster, partially radiative shocks moving through the lower-density gas near the periphery of the clouds. In these shocks dust has been effectively destroyed, while in the slower cloud shocks the dust destruction is incomplete until the recombination zone of the shock has been reached. These dense interstellar clouds provide a sampling of the general interstellar medium (ISM) of the LMC. Our shock analysis allows us to make a new determination of the ISM chemical composition in N, O, Ne, S, Cl, and Ar, and to obtain accurate estimates of the fraction of refractory grains destroyed. From the derived cloud shock parameters, we estimate cloud masses and show that the clouds previously existed as typical self-gravitating Bonnor-Ebert spheres into which converging cloud shocks are now being driven.