Recent research attention for relation extraction has been paid to the dialogue scenario, i.e., dialogue-level relation extraction (DiaRE). Existing DiaRE methods either simply concatenate the utterances in a dialogue into a long piece of text, or employ naive words, sentences or entities to build dialogue graphs, while the structural characteristics in dialogues have not been fully utilized. In this work, we investigate a novel dialogue-level mixed dependency graph (D2G) and an argument reasoning graph (ARG) for DiaRE with a global relation reasoning mechanism. First, we model the entire dialogue into a unified and coherent D2G by explicitly integrating both syntactic and discourse structures, which enables richer semantic and feature learning for relation extraction. Second, we stack an ARG graph on top of D2G to further focus on argument inter-dependency learning and argument representation refinement, for sufficient argument relation inference. In our global reasoning framework, D2G and ARG work collaboratively, iteratively performing lexical, syntactic and semantic information exchange and representation learning over the entire dialogue context. On two DiaRE benchmarks, our framework shows considerable improvements over the current state-of-the-art baselines. Further analyses show that the model effectively solves the long-range dependence issue, and meanwhile gives explainable predictions.