The virtual surgery engine represents a crucial research domain within biomedical and information sciences. To address the real-time and realistic demands of virtual surgical robots for soft tissue deformation and cutting, the surface information and internal structure of organ models have been redefined. An enhanced Three-Parameter Mass-Ogden model, which incorporates nonlinearity and viscoelasticity in soft tissues, has been developed based on extended position dynamics. Cluster constraints for filling particles were introduced to improve the smoothness of surgical procedures. The relaxation and creep characteristics of real soft tissues were accounted for by evaluating the responses of various biological tissues to external stress and loads using the HY-0580 high-performance mechanical testing machine. Eight experiments were conducted for each tissue type, and five sets of valid data were averaged and fitted using the Three-Parameter Mass-Ogden mixed model. Surgical simulations were conducted using Abaqus, incorporating Young's modulus, stress-strain relationships, cutting depth, pressure distribution, real-time feedback, and comprehensive visualization. The model's effectiveness was further validated. The surgical platform was integrated into a virtual reality-based digital twin robot simulator for minimally invasive surgery, achieving a surgical operation refresh rate of 78.5 Hz, a visual refresh rate of 60 Hz, and a haptic feedback refresh rate of 1000 Hz. Comparative analysis with the Mass-Spring Model (MSM) and Finite Element Method (FEM) shows our model's superior balance of accuracy and efficiency. MSM is fast but imprecise, while FEM is accurate but computationally intensive.