Underwater Wireless Sensor Networks (UWSNs) play a vital role in ocean monitoring and exploration. However, harsh underwater conditions and frequent topology changes caused by node and sink mobility pose significant challenges for reliable routing. Conventional routing protocols that depend on global route reconstruction and static paths generate excessive control overhead and degrade performance in large-scale underwater environments. In this paper, we propose an energy-efficient virtual cell-based mobile-sink adaptive routing (VC-MAR) protocol for UWSNs. The sensing field is logically partitioned into a three-dimensional grid of virtual cells, where a cell-gateway is elected in each cell to construct a low-overhead routing backbone. To support sink mobility, VC-MAR introduces a localized route-adjustment mechanism that updates only the affected backbone segments rather than reconstructing the entire routing structure. By confining routing updates to neighboring cells influenced by sink movement, the proposed protocol significantly reduces control packet exchanges while ensuring stable and reliable data delivery. Simulation results show that the proposed VC-MAR improves the packet delivery ratio by up to 20% and reduces routing control overhead by about 34% compared with traditional grid-based routing methods. These results confirm the suitability of VC-MAR for dynamic and realistic underwater sensing scenarios.