Secure multi-party computation (SMC) techniques are increasingly more efficient and practical, due in part, to various improvements. For instance, recent research has shown that different protocols that are implemented using different sharing mechanisms (e.g., boolean and arithmetic sharings) can have varying computational and communication costs. Although there are some approaches to automatically mix protocols of different sharing schemes to enhance execution efficiency, none provide a generic optimization framework to discover the least expensive mixed-protocol SMC execution for cloud deployment.In this work, we introduce a generic SMC optimization framework CheapSMC that can invoke any mixed-protocol SMC circuit evaluation tool as a black box to uncover the cheapest SMC cloud deployment option. To do so, CheapSMC computes one-time benchmarks for the target cloud service and gathers performance statistics for basic circuit components. Relying on these statistics, an optimization layer of CheapSMC invokes several heuristics to find the cheapest mix-protocol circuit evaluation. Subsequently, the optimized circuit is passed to a mixed-protocol SMC tool for actual executable generation. Our empirical results, gathered by running cases studies on large range of complexity in data volume and functions for computation, show that significant cost savings can be achieved via our optimization framework in comparison to the state-of-the-art.