Large Language Models (LLMs) can generate plausible test code. Intuitively they generate this by imitating tests seen in their training data, rather than reasoning about execution semantics. However, such reasoning is important when applying mutation testing, where individual tests need to demonstrate differences in program behavior between a program and specific artificial defects (mutants). In this paper, we evaluate whether Scientific Debugging, which has been shown to help LLMs when debugging, can also help them to generate tests for mutants. In the resulting approach, LLMs form hypotheses about how to kill specific mutants, and then iteratively generate and refine tests until they succeed, all with detailed explanations for each step. We compare this method to three baselines: (1) directly asking the LLM to generate tests, (2) repeatedly querying the LLM when tests fail, and (3) search-based test generation with Pynguin. Our experiments evaluate these methods based on several factors, including mutation score, code coverage, success rate, and the ability to identify equivalent mutants. The results demonstrate that LLMs, although requiring higher computational cost, consistently outperform Pynguin in generating tests with better fault detection and coverage. Importantly, we observe that the iterative refinement of test cases is important for achieving high-quality test suites.