With the maturity of cloud computing technology in terms of reliability and efficiency, a large number of services have migrated to the cloud platform. To convenient access to the services and protect the privacy of communication in the public network, three-factor Mutual Authentication and Key Agreement (MAKA) protocols for multi-server architectures gain wide attention. However, most of the existing three-factor MAKA protocols don't provide a formal security proof resulting in various attacks on the related protocols, or they have high computation and communication costs. And most of the three-factor MAKA protocols haven't a dynamic revocation mechanism, which leads to malicious users can not be promptly revoked. To address these drawbacks, we propose a provable dynamic revocable three-factor MAKA protocol that achieves the user dynamic management using Schnorr signatures and provides a formal security proof in the random oracle. Security analysis shows that our protocol can meet various demands in the multi-server environments. Performance analysis demonstrates that the proposed scheme is well suited for computing resource constrained smart devices. The full version of the simulation implementation proves the feasibility of the protocol.