The relaxation dynamics of a homogeneous poly(styrene)-poly(butadiene) star diblock copolymer melt following step shear flow is studied as its temperature is lowered through the microphase separation temperature (MST). Transient Raman scattering, birefringence, and mechanical rheometry measurements are used to investigate segment and composition pattern relaxation dynamics. The birefringence was determined to be primarily form birefringence, and its relaxation rate was found to decrease dramatically in the vicinity of the MST. At temperatures close to the MST, the shear stress, first normal stress difference, and segment orientation anisotropy (from Raman scattering measurements) relaxation rates also decreased. Slowing down of the first normal stress difference and segment orientation anisotropy relaxations was found to be less dramatic than that of the birefringence relaxation but more pronounced than that of the shear stress relaxation. A decrease in the relaxation rate of segment orientation anisotropy close to the MST is proposed to result from the coupling of segmental and composition pattern relaxations due to tethering of chain segments to the domain interface.