The ability of LLM agents to plan and invoke tools exposes them to new safety risks, making a comprehensive red-teaming system crucial for discovering vulnerabilities and ensuring their safe deployment. We present SIRAJ: a generic red-teaming framework for arbitrary black-box LLM agents. We employ a dynamic two-step process that starts with an agent definition and generates diverse seed test cases that cover various risk outcomes, tool-use trajectories, and risk sources. Then, it iteratively constructs and refines model-based adversarial attacks based on the execution trajectories of former attempts. To optimize the red-teaming cost, we present a model distillation approach that leverages structured forms of a teacher model's reasoning to train smaller models that are equally effective. Across diverse evaluation agent settings, our seed test case generation approach yields 2 -- 2.5x boost to the coverage of risk outcomes and tool-calling trajectories. Our distilled 8B red-teamer model improves attack success rate by 100%, surpassing the 671B Deepseek-R1 model. Our ablations and analyses validate the effectiveness of the iterative framework, structured reasoning, and the generalization of our red-teamer models.