Matching the daytime visible and nighttime infrared person images, namely visible infrared person re-identification (VI-ReID), is a challenging cross-modality retrieval problem. Due to the difficulty of data collection and annotation in nighttime surveillance, VI-ReID usually suffers from noise problems, making it challenging to directly learn part discriminative features. In order to improve the discriminability and enhance the robustness against noisy images, this paper proposes a novel dynamic tri-level relation mining (DTRM) framework by simultaneously exploring channel-level, part-level intra-modality, and graph-level cross-modality relation cues. To address the misalignment within the person images, we design an intra-modality weighted-part attention (IWPA) to construct part-aggregated representation. It adaptively integrates the body part relation into the local feature learning with a residual batch normalization (RBN) connection scheme. Besides, a cross-modality graph structured attention (CGSA) is incorporated to improve the global feature learning by utilizing the contextual relation between images from two modalities. This module reduces the negative effects of noisy images. To seamlessly integrate two components, a parameter-free dynamic aggregation strategy is designed in a progressive joint learning manner. To further improve the performance, we additionally design a simple yet effective channel-level learning strategy by exploiting the rich channel information of visible images, which significantly reinforces the performance without modifying the network structure or changing the training process. Extensive experiments on two visible infrared re-identification datasets have verified the effectiveness under various settings. Code is available at: https://github.com/mangye16/DDAG