A system that implements a data storage service may maintain tables in a data store on behalf of clients. The service may maintain table data in multiple replicas of partitions of the data that are stored on respective computing nodes in the system. In response to detecting a failure or fault condition, or receiving a service request from a client to move or copy a partition replica, the data store may copy a partition replica to another computing node using a physical copy mechanism. The physical copy mechanism may copy table data from physical storage locations in which it is stored to physical storage locations allocated to a destination replica on the other computing node. During copying, service requests to modify table data may be logged and applied to the replica being copied. A catch-up operation may be performed to apply modification requests received during copying to the destination replica.