Highly-filled elastomers such as solid propellants exhibit a complex nonlinear viscoelastic behavior. The microstructural origin of this behavior is difficult to ascertain with macroscopic observations. This article aims at identifying the deformation mechanisms of a solid propellant by measuring the change in segmental mobility with deformation. The novelty lies in the use of 1H Nuclear Magnetic Resonance (NMR) spectrometry to investigate the spin–spin relaxation times T2 of a solid propellant. In addition, the effect of strain on T2 is measured using a specific setup transmitting the loading of the tensile machine to the sample inside the NMR apparatus. We compare isolated components, unfilled binders, and solid propellants varying in composition according to a design of experiments. The design of experiments determines the influences of the filler fraction, the amount of curing agents, the plasticizer content, and the presence of filler–binder bonding agents, on the segmental mobilities. The propellant protons can be schematically divided into three segmental mobilities corresponding to distinct relaxation times. The short times correspond to the severely restricted segments situated around cross-links or fillers. The intermediate relaxation times correspond to segments of polymer chains linked at both ends. Finally, the long relaxation times correspond to the highly mobile segments of polymers (dangling ends) and to the plasticizer molecules. The influence of strain on the relaxation times shows that the polymer network is stretched between the fillers while part of the polymer in the sol fraction is immobilized. In addition, chain sliding on the filler surface and breaking of filler–binder links can occur.