Molecular dynamics simulations are carried out to explore the dynamical crossover phenomenon in strongly confined and mildly supercooled water in graphene oxide nanopores. Since the extent of hydrophilicity can be varied on graphene oxide surfaces, they offer energetically heterogeneous environments that can potentially modulate the rotational and translational relaxation dynamics of confined water. The influence of the physicochemical nature of the graphene oxide surface on the dynamical transitions is investigated by varying the extent of hydrophobicity on the confining surfaces placed at an intersurface separation of 10 angstrom. Water forms two distinct layers in contact with the graphene oxide surface at this separation. All dynamical quantities show a typical slowing down as the temperature is lowered from 298 to 200 K; however, the nature of the transition is a distinct function of the surface type. Water confined between surfaces consisting of alternating hydrophilic and hydrophobic regions exhibit a strong-to-strong dynamical transition in the diffusion coefficients and rotational relaxation times at a crossover temperature of 237 K and show a fragile-to-strong transition in the alpha-relaxation time at 238 K. The observed crossover temperature is higher than the freezing point of the SPC/E water model used in this study, indicating that these dynamical transitions can occur with mild supercooling under strong confinement in the absence of bulk-like water. In contrast, water confined in a hydrophilic nanopore shows a single Arrhenius energy barrier over the entire temperature range. Our results indicate that in addition to confinement, the nature of the surface can play a critical role in determining the dynamical transitions for water upon supercooling.