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While achieving tremendous success in various fields, existing multi-agent reinforcement learning (MARL) with a black-box neural network makes decisions in an opaque manner that hinders humans from understanding the learned knowledge and how input observations influence decisions. In contrast, existing interpretable approaches usually suffer from weak expressivity and low performance. To bridge this gap, we propose MIXing Recurrent soft decision Trees (MIXRTs), a novel interpretable architecture that can represent explicit decision processes via the root-to-leaf path and reflect each agent's contribution to the team. Specifically, we construct a novel soft decision tree using a recurrent structure and demonstrate which features influence the decision-making process. Then, based on the value decomposition framework, we linearly assign credit to each agent by explicitly mixing individual action values to estimate the joint action value using only local observations, providing new insights into interpreting the cooperation mechanism. Theoretical analysis confirms that MIXRTs guarantee additivity and monotonicity in the factorization of joint action values. Evaluations on complex tasks like Spread and StarCraft II demonstrate that MIXRTs compete with existing methods while providing clear explanations, paving the way for interpretable and high-performing MARL systems.