Novel methods in biological physics are becoming critical in clinical application, to functionally interpret cancer genomic alterations. For Chronic Lymphocytic Leukemia (CLL), a heterogeneous disease of B-lymphocytes maturing under constitutive B-cell receptor (BCR) stimulation, the functional role of diverse clonal mutations remains largely unknown. We present here a combination of single-cell measurements and computational modeling to demonstrate that alterations in BCR signaling dynamics underlie the progression of B-cells toward malignancy. We apply nonlinear dynamics methods to reveal emergent dynamic features, namely bimodality, hypersensitivity, and hysteresis, in the BCR signaling pathway of primary CLL B-cells. We demonstrate that such signaling abnormalities in CLL quantitatively derive from BCR clustering and constitutive signaling with positive feedback reinforcement, as demonstrated through single-cell analysis of signaling motifs, computational modeling, and superresolution imaging. Such dysregulated signaling segregates CLL patients by disease severity and clinical presentation. Our findings provide a novel quantitative framework and illustrate how approaches borrowed from biological physics help assess complex and heterogeneous cancer pathology.