Cutting is a recurring operation in robotic au tomation, from food preparation to surgical tissue resection. For highly compliant targets, blade motion may deform or displace the material rather than advance the intended cut, while progressive failure changes load transfer and subsequent tool tissue interaction. A computational description must therefore connect cut formation to the evolving mechanical response, rather than specifying the incision independently of material failure. We present STC-MPM (Soft Tissue Cutting with the Material Point Method), a framework that couples finite-strain deformation, history-driven continuum damage, and configurable post-failure treatment. Damage initiates only when a tensile strain history exceeds a material threshold within the blade process zone. Progressive degradation changes stress transmission before the post-failure policy is applied, while the remaining tissue continues to deform, move, and interact with the tool. Numerical scalpel studies using delayed particle deactivation follow this response through insertion and withdrawal. Under identical blade motion, reducing the damage-rate limit leaves the first recorded damage time unchanged but delays and increases peak reaction force, delays particle deactivation, and increases the fixed-cohort displacement statistic at maximum insertion. The matched comparison illustrates how post-initiation failure evolution alters subsequent tool loading and recorded material motion. STC-MPM thus supports joint analysis of cut formation and accompanying tissue response without a pre-inserted cutting interface.

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