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We present an algorithm that allows a user within a virtual environment to perform real-time unconstrained cuts or consecutive tears, i.e., progressive, continuous fractures on a deformable rigged and soft-body mesh model in high-performance 10ms. In order to recreate realistic results for different physically-principled materials such as sponges, hard or soft tissues, we incorporate a novel soft-body deformation, via a particle system layered on-top of a linear-blend skinning model. Our framework allows the simulation of realistic, surgical-grade cuts and continuous tears, especially valuable in the context of medical VR training. In order to achieve high performance in VR, our algorithms are based on Euclidean geometric predicates on the rigged mesh, without requiring any specific model pre-processing. The contribution of this work lies on the fact that current frameworks supporting similar kinds of model tearing, either do not operate in high-performance real-time or only apply to predefined tears. The framework presented allows the user to freely cut or tear a 3D mesh model in a consecutive way, under 10ms, while preserving its soft-body behaviour and/or allowing further animation.