Methyl-methacrylate-grafted natural rubber was prepared by free radical polymerization of methyl methacrylate in natural rubber latex, and their structure and dynamics were investigated by dynamic mechanical analysis and solid-state nuclear magnetic resonance (NMR). Samples were prepared by chemical initiation and high energy radiation. The changes of glass transition temperature and tan delta max with different total polymethyl methacrylate (PMMA) content are reported. The effect of the change in composition in copolymers on tan delta peak width, tan delta max, and area under the tan delta curve are used to understand the miscibility and damping properties. Solid-state C-13-NMR measurements were carried out to determine several relaxation time parameters, such as rotating frame and laboratory frame proton and carbon relaxation times. Cross polarization times and carbon relaxation times were interpreted based on the changes in the molecular motion. Proton relaxation times were interpreted based on the heterogeneity of the matrix. Results confirmed phase separation and a presence of an interfacial region.