JavaScript (JS) engines implement complex language semantics and optimization strategies to support the dynamic nature of JS, making them difficult to test thoroughly and prone to subtle, security-critical bugs. Existing fuzzers often struggle to generate diverse and valid test cases. They either rely on syntax-level mutations that lack semantic awareness or perform limited, local mutations on concrete code, thus failing to explore deeper, more complex program behaviors. This paper presents TemuJs, a novel fuzzing framework that performs extraction and mutation at a high level, operating on abstract templates derived from real-world JS programs. These templates capture coarse-grained program structures with semantic placeholders, enabling semantics-aware mutations that preserve the high-level intent of the original code while diversifying its behavior. By decoupling mutation from concrete syntax and leveraging a structured intermediate representation for the templates, TemuJs explores a broader and more meaningful space of program behaviors. Evaluated on three major JS engines, namely, V8, SpiderMonkey, and JavaScriptCore, TemuJs discovers 44 bugs and achieves a 10.3% increase in edge coverage compared to state-of-the-art fuzzers on average. Our results demonstrate the efficacy of high-level, template-mutation fuzzing in testing JS engines.