Functional interpretation of genomic variation is critical to understanding human disease, but it remains difficult to predict the effects of specific mutations on protein interaction networks and the phenotypes they regulate. We describe an analytical framework based on multiscale statistical mechanics that integrates genomic and biophysical data to model the human SH2-phosphoprotein network in normal and cancer cells. We apply our approach to data in The Cancer Genome Atlas (TCGA) and test model predictions experimentally. We find that mutations mapping to phosphoproteins often create new interactions but that mutations altering SH2 domains result almost exclusively in loss of interactions. Some of these mutations eliminate all interactions, but many cause more selective loss, thereby rewiring specific edges in highly connected subnetworks. Moreover, idiosyncratic mutations appear to be as functionally consequential as recurrent mutations. By synthesizing genomic, structural and biochemical data, our framework represents a new approach to the interpretation of genetic variation.