The nanostructure changes associated with stress dissipation in a tough, supramolecular hydrogel were determined by small-angle neutron scattering (SANS) and compared with stress-relaxation measurements to understand the molecular origin of the toughness. The hydrogels were formed from random copolymers of N,N-dimethylacrylamide (DMA) and 2-(N-ethylperfluorooctane sulfonamido)ethyl acrylate (FOSA), which exhibit a microphase-separated morphology with physical cross-links formed by the FOSA nanodomains connected by DMA chains. The stress relaxation behavior following a step strain was fit using seven exponentials with relaxation times that spanned 5 orders of magnitude. The deformation and relaxation of the FOSA nanodomains and network chains were independently resolved using two different contrasts with SANS experiments. Stretching of the hydrogel produced anisotropic scattering at both contrasts examined. The DMA network chains relaxed to an isotropic state at a fast rate that corresponded to the shorter stress relaxation time, while the nanodomain structure relaxed slower and did not fully relax after 7 h. These SANS measurements provide correlations between relaxations at the macroscopic (stress) and microscopic (network chains and nanodomains) scales.