We present a novel approach to fluid simulation over complex dynamic geometry designed for the specific context of virtual surgery simulation. The method combines a surface-based fluid simulation model with a multi-layer depth peeling representation to allow realistic yet efficient simulation of bleeding on complex surfaces undergoing geometry and topology modifications. Our implementation allows for fast fluid propagation and accumulation over the entire scene, and runs on the GPU at a constant low cost that is independent of the amount of blood in the scene. The proposed bleeding simulation is integrated in a complete simulator for brain tumor resection, where trainees have to manage blood aspiration and tissue/vessel cauterization while they perform virtual surgery tasks.