Underwater acoustic sensor networks (UW-ASNs) have been attracting more and more research interests recently due to their various promising applications. For the applications such as the environmental monitoring and event detection services, there will be a large amount of data generated in UW-ASNs. To reliably store and efficiently retrieve the generated data, data-centric storage which stores the same type of data in a specific region and facilitates data retrieval is regarded as an attractive solution. In this paper, we focus on the cross-layer design for the data transmissions of data-centric storage in UW-ASNs. In order to minimize the network transmission delay in a specific data-centric storage procedure, we introduce the spatial reuse concept into the cross-layer design, where multiple communication links are permitted to perform data transmission simultaneously with efficient interference management. Then, we propose a spatial reuse TDMA based cross-layer (SRC-TDMA) protocol by jointly taking data routing and resource scheduling into consideration. Simulation results verify that our proposed SRC-TDMA protocol can significantly reduce the network transmission delay compared with the traditional TDMA protocol and the interference graph based TDMA (IG-TDMA) protocol.