Cancer growth and invasion are complex processes involving biochemical and mechanical interactions. Here, we focus on the mechanisms underlying collective invasion in the early stages of luminal breast cancer, during which cohesive strands of cancer cells protrude into the surrounding extracellular matrix (ECM). Previous experimental findings emphasize the role of ECM mechanics, with invasion-induced alignment of collagen fibers and tension buildup, and suggest that invasion is mediated by a biomechanical feedback between cancer cells and the surrounding fibrous matrix. However, the mechanistic nature of this feedback is poorly understood. To address this question, here we combine observations in breast cancer organoids with mathematical and computational modeling. First, we perform quantitative full-field analysis of the kinematics of collective invasion, allowing us to reconstruct the flow fields of cells and the surrounding ECM. This analysis shows that, unexpectedly, invasion is accompanied by enhanced ECM degradation by cells, with invasive strands corresponding to locations of faster proteolysis, as well as regions where the ECM is tense and collagen fibers aligned. Second, we develop a continuum theory based on Onsager’s variational approach for irreversible thermodynamics for the nonlinear interplay between the ECM (modeled as a hyperelastic solid), the cancer organoid (modeled as a growing viscous fluid), and cell degradation at the ECM-organoid interface. We show that ECM degradation at this interface against a tense ECM is necessarily an active process, and that activity must be higher at invasive strands. These observations lead us to hypothesize that the active degradation process is mechanosensitive. With this hypothesis, our theory explains the emergence of the invasive phenotype and the collective invasion mechanism as a self-organized pattern formation resulting from a mechano-biological instability. Third, to test the theoretical model quantitatively, we develop a finite element computational framework. This approach is based on an unfitted description of the moving interface with a quad-tree background mesh and is built on a Nitsche-Onsager variational formulation of the problem. Because our model's degradation activity depends on tractions at the interface, we pay particular attention to the numerical accuracy of those tractions.