Personal data stored in the Cloud may contain account numbers, passwords, notes, and other important information that could be used and misused by a miscreant, a competitor, or a court of law. These data are cached, copied, and archived by Cloud Service Providers (CSPs), often without users' authorization and control. Self-destructing data mainly aims at protecting the user data's privacy. All the data and their copies become destructed or unreadable after a user-specified time, without any user intervention. In addition, the decryption key is destructed after the user-specified time. In this paper, we present SeDas, a system that meets this challenge through a novel integration of cryptographic techniques with active storage techniques based on T10 OSD standard. We implemented a proof-of-concept SeDas prototype. Through functionality and security properties evaluations of the SeDas prototype, the results demonstrate that SeDas is practical to use and meets all the privacy-preserving goals described. Compared to the system without self-destructing data mechanism, throughput for uploading and downloading with the proposed SeDas acceptably decreases by less than 72%, while latency for upload/download operations with self-destructing data mechanism increases by less than 60%.