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Visible-infrared person re-identification (VI-ReID) is a challenging cross-modality pedestrian retrieval problem. Due to the large intra-class variations and cross-modality discrepancy with large amount of sample noise, it is difficult to learn discriminative part features. Existing VI-ReID methods instead tend to learn global representations, which have limited discriminability and weak robustness to noisy images. In this paper, we propose a novel dynamic dual-attentive aggregation (DDAG) learning method by mining both intra-modality part-level and cross-modality graph-level contextual cues for VI-ReID. We propose an intra-modality weighted-part attention module to extract discriminative part-aggregated features, by imposing the domain knowledge on the part relationship mining. To enhance robustness against noisy samples, we introduce cross-modality graph structured attention to reinforce the representation with the contextual relations across the two modalities. We also develop a parameter-free dynamic dual aggregation learning strategy to adaptively integrate the two components in a progressive joint training manner. Extensive experiments demonstrate that DDAG outperforms the state-of-the-art methods under various settings.