We present a new method for model-based mutation-driven test case generation. Mutants are generated by making small syntactical modifications to the model or source code of the system under test. A test case kills a mutant if the behavior of the mutant deviates from the original system when running the test. In this work, we use hyperproperties-which allow to express relations between multiple executions-to formalize different notions of killing for both deterministic as well as non-deterministic models. The resulting hyperproperties are universal in the sense that they apply to arbitrary reactive models and mutants. Moreover, an off-the-shelf model checking tool for hyperproperties can be used to generate test cases. We evaluate our approach on a number of models expressed in two different modeling languages by generating tests using a state-of-the-art mutation testing tool.