The mechanical properties of the double gyroid (DG) cubic phase in glassy-rubbery block copolymer systems are examined. The stress-strain properties of an isoprene-rich polystyrene/polyisoprene/polystyrene (SIS) triblock and a polystyrene/polyisoprene (SI) starblock DG, both comprised of two separate interpenetrating glassy networks embedded in rubbery matrices, are compared to those of the sphere, cylinder, and lamellar morphologies. This 9-dimensionally interpenetrating periodic nanocomposite is found to have superior properties over those of its classical counterparts, attributable to the morphology rather than to the volume fraction of the glassy component, the architecture of the molecule, or the molecular weight. The DG is the only polygranular/isotropic thermoplastic elastomer morphology which exhibits necking and drawing and which requires considerably higher stresses for deformation up to 200% strain than any of the three classical microdomain morphologies. The deformation behavior of the DG is further investigated as a function of applied strain using in situ synchrotron small-angle X-ray scattering. Yielding and necking are observed at similar to 20% strain, accompanied by sudden changes in the SAXS patterns: the characteristic Bragg rings of the DG disappear and are replaced by a lobe pattern containing streaks and diffuse scattering. Analysis of the {211} reflection in the SAXS data indicates that PS networks play a large role in governing the deformation behavior. The necking behavior of the DG suggests a different deformation mechanism. The DG samples recover both microscopically and macroscopically upon unloading and annealing, indicating that the complex interconnected nanocomposite structure was not permanently damaged, even after having been stretched to 600% strain.