Dexterous manipulation requires high-dimensional control policies to accomplish complex contact-rich tasks while simultaneously satisfying multiple safety requirements, such as joint limits, unsafe finger configurations, arm collisions, and unstable object interactions. Constrained reinforcement learning (RL) provides a principled framework for incorporating these requirements into dexterous manipulation policy learning. However, existing constrained RL methods for dexterous manipulation primarily focus on cumulative cost constraints and struggle to simultaneously handle multiple heterogeneous constraints during dexterous policy learning. In this work, we propose Multi-constraint Dexterous Policy Optimization (MDPO) for safe dexterous manipulation. We first formulate dexterous manipulation as a multi-constraint policy optimization problem involving both cumulative cost constraints and state-wise cost constraints. Based on this formulation, we integrate multi-constraint projection into the dexterous manipulation policy optimization process. Specifically, we employ constraint-specific policy projections to map the intermediate policy that maximizes task performance onto the feasible regions defined by the cumulative cost constraint and the state-wise cost constraint. Extensive experiments on ReDMan, including safe joint control, finger safety, and grasping tasks, demonstrate that MDPO achieves superior constraint satisfaction while maintaining competitive task performance compared with the baselines. Our code is available at this link.

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