Mutation testing is one of the most powerful approaches for evaluating quality of test suites. However, mutation testing is also one of the most expensive testing approaches. This paper presents Regression Mutation Testing (ReMT), a new technique to speed up mutation testing for evolving systems. The key novelty of ReMT is to incrementally calculate mutation testing results for the new program version based on the results from the old program version; ReMT uses a static analysis to check which results can be safely reused. ReMT also employs a mutation-specific test prioritization to further speed up mutation testing. We present an empirical study on six evolving systems, whose sizes range from 3.9KLoC to 88.8KLoC. The empirical results show that ReMT can substantially reduce mutation testing costs, indicating a promising future for applying mutation testing on evolving software systems.