An increasing number of businesses are replacing their data storage and computation infrastructure with cloud services. Likewise, there is an increased emphasis on performing analytics based on multiple datasets obtained from different data sources. While ensuring security of data and computation outsourced to a third party cloud is in itself challenging, supporting analytics using data distributed across multiple, independent clouds is even further from trivial. In this paper we present CloudMine, a cloud-based service which allows multiple data owners to perform privacy-preserved computation over the joint data using their clouds as delegates. CloudMine protects data privacy with respect to semi-honest data owners and semi-honest clouds. It furthermore ensures the privacy of the computation outputs from the curious clouds. It allows data owners to reliably detect if their cloud delegates have been lazy when carrying out the delegated computation. CloudMine can run as a centralized service on a single cloud, or as a distributed service over multiple, independent clouds. CloudMine supports a set of basic computations that can be used to construct a variety of highly complex, distributed privacy-preserving data analytics. We demonstrate how a simple instance of CloudMine (secure sum service) is used to implement three classical data mining tasks (classification, association rule mining and clustering) in a cloud environment. We experiment with a prototype of the service, the results of which suggest its practicality for supporting privacy-preserving data analytics as a (multi) cloud-based service.