In this study, compressive hysteretic damping properties of carboxylated nitrile rubber (XNBR) and its composites containing multiwalled carbon nanotubes (MWNT) were investigated at high strains by Universal Testing Machine (UTM) and at low strains by Dynamic Mechanical Analyzer (DMA). Degree of damping is less than the neat XNBR at low MWNT loading and it increases significantly at higher loading. At constant MWNT loading, the extent of damping depends on applied strain. Mullins effect is observed in both neat XNBR and composites due to the presence of ionic clusters. Differential Scanning Calorimetry (DSC) and X-ray diffraction analysis (XRD) confirm the reversible nature of the ionic cluster formation/deformation. Deformation of ionic clusters and nanotube agglomerates contribute to the overall increase in damping. Morphology characterization by Transmission Electron Microscope (TEM) reveals agglomeration of nanotubes at higher loading levels. A schematic diagram about the structural changes due to application of heat and stress is proposed. The results would be of great assistance in the design of application specific composites for various engineering applications.