Data has become a valuable resource that drives new business models and creates enormous business value. However, under the current data ownership model, many data-driven applications arbitrarily collect and overuse user data for commercial purposes, resulting in increased incidents of data breaches and data misuse. In this paper, we present Data Interoperating Architecture (DIA) that decouples applications and user data to give back data ownership to users. We design Data Interoperating System (DIS) based on blockchain, identity system, and identifier system to solve the key issues of data interoperation: identity management, data identification, data discovery, and data ownership protection. DIS provides services without collecting or accessing data, keeping data under the control of its owner. We formalize the interactions among components in DIA as Data Interoperating Protocol (DIP), which facilitates applications and personal data stores to be compatible with DIS. We develop a prototype of DIS and evaluate the system performance under adopted techniques. Experimental results show that DIS is effective and efficient in supporting real-world data interoperation.