We investigate the mechanical properties of triblock copolymers with oriented double gyroid (DG) morphology in poly(styrene-b-isoprene-b-styrene) (SIS) triblock copolymers by deforming textured samples along both the [111] direction and transverse to this direction. The modulus anisotropy for the two directions of this cubic material is approximately a factor of 5. Deformation along [111] causes the sample to form a distinct neck and draw, while the deformation in the transverse direction proceeds without neck formation. In addition, the mechanical hysteresis of the [111] stretch is 50% higher than that transverse to the [111] direction. Upon unloading and annealing above the polystyrene Tg, the DG structure recovers fully, both macroscopically and microscopically. The mechanical properties of the DG are compared to those of the classical block copolymer morphologies to gain insight into the deformation mechanism.