Software testing is a complex and costly stage during the software development lifecycle. Nowadays, there is a wide variety of solutions to reduce testing costs and improve test quality. Focussing on test case generation, Dynamic Symbolic Execution (DSE) is used to generate tests with good structural coverage. Regarding test suite evaluation, Mutation Testing (MT) assesses the detection capability of the test cases by introducing minor localised changes that resemble real faults. DSE is however known to produce tests that do not have good mutation detection capabilities: in this paper, the authors set out to solve this by combining DSE and MT into a new family of approaches that the authors call Mutation-Inspired Symbolic Execution (MISE). First, this known result on a set of open source programs is confirmed: DSE by itself is not good at killing mutants, detecting only 59.9% out of all mutants. The authors show that a direct combination of DSE and MT (naive MISE) can produce better results, detecting up to 16% more mutants depending on the programme, though at a high computational cost. To reduce these costs, the authors set out a roadmap for more efficient versions of MISE, gaining its advantages while avoiding a large part of its additional costs.