SysML models are widely used for designing and analyzing complex systems. Model-based design methods often require successive modifications of the models, whether for incrementally refining the design (e.g. in agile development methods) or for testing different design options. Such modifications, or mutations, are also used in mutation-based testing approaches. However, the definition of mutation operators can be a complex issue and applying them to models is sometimes performed by hand: this is time consuming and error prone. The paper addresses this issue thanks to the introduction of AMULET, the first mutation language for SysML. AMULET encompasses the modifications targeting SysML block and state-machine diagrams, and is supported by a compiler the paper presents. This compiler is integrated in TTool, an open-source SysML toolkit, enabling the full support of design methods including model design, mutation and verification tasks in a unique toolkit. The paper also introduces two case-studies providing concrete examples of AMULET use for modeling vulnerabilities and cyber attacks, and highlighting the benefits of AMULET for SysML mutations.