A major goal of cancer biology is to understand the mechanisms underlying tumorigenesis driven by somatically acquired mutations. Existing computational approaches focus on either scoring the pathogenicity of mutations or characterizing their effects at specific scales. Here, we established a unified computational framework, NetFlow3D, that systematically maps the multiscale mechanistic effects of somatic mutations in cancer. The establishment of NetFlow3D hinges upon the Human Protein Structurome, a complete repository we first compiled that incorporates the 3D structures of every single protein as well as the binding interfaces for all known PPIs in humans. The vast majority of 3D structural information was resolved by recent deep learning algorithms. By applying NetFlow3D to 415,017 somatic protein-altering mutations in 5,950 TCGA tumors across 19 cancer types, we identified 1,656 intra- and 3,343 inter-protein 3D clusters of mutations throughout the Human Protein Structurome, of which ~50% would not have been found if using only experimentally-determined protein structures. These 3D clusters have converging effects on 377 cellular subnetworks. Compared to canonical PPI network analyses, NetFlow3D achieved a 5.5-fold higher statistical power for identifying significantly dysregulated subnetworks. The majority of identified subnetworks were previously obscured by the overwhelming background noise of non-clustered passenger mutations, including portions of non-canonical PRC1, mediator complex, MCM2-7 complex, neddylation of cullins, complement system, TRiC, etc. NetFlow3D and our pan-cancer results can be accessed from http://netflow3d.yulab.org. This work shows that mapping how individual mutations act across scales requires the integration of their local spatial organization on protein structures and their global topological organization in the PPI network.