A system that implements a scalable data storage service may maintain tables in a data store on behalf of storage service clients. The service may maintain table data in multiple replicas of partitions that are stored on respective computing nodes in the system. In response to detecting an anomaly in the system, detecting a change in data volume on a partition or service request traffic directed to a partition, or receiving a service request from a client to split a partition, the data storage service may create additional copies of a partition replica using a physical copy mechanism. The data storage service may issue a split command defined in an API for the data store to divide the original and additional replicas into multiple replica groups, and to configure each replica group to maintain a respective portion of the table data that was stored in the partition before the split.