Atomistic molecular dynamics (MD) simulations at different temperatures ranging from 160 to 300 K have been carried out to explore the correlated dynamical transitions of a single-stranded DNA (ss-DNA) oligomer with heterogeneous distribution of nucleobases, 5'-CGCGAATTCGCG-3', and that of its hydration water. The calculations reveal a distinct dynamical crossover of the DNA oligomer associated with abrupt changes of motions of its atoms at around 200-220 K. Importantly, it is found from calculated water diffusivities and relaxation times that the hydration water molecules also exhibit a crossover within 210-220 K. This indicates that the dynamical crossover of the DNA strand is coupled with that exhibited by its hydration water. In addition, another crossover point for the surface water molecules has been found around 180-185 K with the water layer exhibiting highly frozen dynamics. The rearrangement of hydrogen bond network that occurs due to population transition from two-coordinated to four-coordinated tetrahedrally arranged water molecules at the interface with lowering of temperature is found to be the microscopic origin of such correlated two-step dynamic crossovers of hydration water. Such modified hydrogen bonding results in transformation of hydration layer water structuring from high density to low density liquid under supercooled conditions.