Embodied agents powered by large language models (LLMs) inherit advanced planning capabilities; however, their direct interaction with the physical world exposes them to safety vulnerabilities. In this work, we identify four key reasoning stages where hazards may arise: Task Understanding, Environment Perception, High-Level Plan Generation, and Low-Level Action Generation. We further formalize three orthogonal safety constraint types (Factual, Causal, and Temporal) to systematically characterize potential safety violations. Building on this risk model, we present SafeMindBench, a multimodal benchmark with 5,558 samples spanning four task categories (Instr-Risk, Env-Risk, Order-Fix, Req-Align) across high-risk scenarios such as sabotage, harm, privacy, and illegal behavior. Extensive experiments on SafeMindBench reveal that leading LLMs (e.g., GPT-4o) and widely used embodied agents remain susceptible to safety-critical failures. To address this challenge, we introduce SafeMindAgent, a modular Planner-Executor architecture integrated with three cascaded safety modules, which incorporate safety constraints into the reasoning process. Results show that SafeMindAgent significantly improves safety rate over strong baselines while maintaining comparable task completion. Together, SafeMindBench and SafeMindAgent provide both a rigorous evaluation suite and a practical solution that advance the systematic study and mitigation of safety risks in embodied LLM agents.