Relation triplet extraction (RTE) is a fundamental while challenging task in knowledge acquisition, which identifies and extracts all triplets from unstructured text.Despite the recent advancements, the deep integration of the entity-, relation-and triplet-specific information remains a challenge.In this paper, we propose a Graph-based Mixture-of-Experts mutual learning framework for RTE, namely RTE-GMoE, to address this limitation.As a model-agnostic framework, RTE-GMoE distinguishes itself by including and modeling the mutual interactions among three vital taskspecific experts: entity expert, RTE expert, and relation expert.RTE expert corresponds to the main RTE task and can be implemented by any model and the other two correspond to the two auxiliary tasks: entity recognition and relation extraction.We construct an expert graph and achieve comprehensive and adaptive graph-based MoE interactions with a novel mutual learning mechanism.In our framework, these experts perform knowledge extractions collaboratively via dynamic information exchange and knowledge sharing.We conduct extensive experiments on four state-ofthe-art backbones and evaluate them on several widely-used benchmarks.The results demonstrate that our framework brings consistent and promising improvements on all backbones and benchmarks.Component study and model analysis further verify the effectiveness and advantages of our method.