Histopathology image-based survival prediction aims to provide a precise assessment of cancer prognosis and can inform personalized treatment decision-making in order to improve patient outcomes. However, existing methods cannot automatically model the complex correlations between numerous morphologically diverse patches in each whole slide image (WSI), thereby preventing them from achieving a more profound understanding and inference of the patient status. To address this, here we propose a novel deep learning framework, termed dual-stream multi-dependency graph neural network (DM-GNN), to enable precise cancer patient survival analysis. Specifically, DM-GNN is structured with the feature updating and global analysis branches to better model each WSI as two graphs based on morphological affinity and global co-activating dependencies. As these two dependencies depict each WSI from distinct but complementary perspectives, the two designed branches of DM-GNN can jointly achieve the multi-view modeling of complex correlations between the patches. Moreover, DM-GNN is also capable of boosting the utilization of dependency information during graph construction by introducing the affinity-guided attention recalibration module as the readout function. This novel module offers increased robustness against feature perturbation, thereby ensuring more reliable and stable predictions. Extensive benchmarking experiments on five TCGA datasets demonstrate that DM-GNN outperforms other state-of-the-art methods and offers interpretable prediction insights based on the morphological depiction of high-attention patches. Overall, DM-GNN represents a powerful and auxiliary tool for personalized cancer prognosis from histopathology images and has great potential to assist clinicians in making personalized treatment decisions and improving patient outcomes.