The development of advanced soft robotics is crucial for delicate medical operations, as traditional rigid robots lack the flexibility required for such procedures. However, the application of nonlinear time-varying dynamics mechanisms to achieve accurate deformation control still faces challenges. In this study, we address the design of a surgical-tool deformation controller for minimally invasive procedures and propose a collaborative framework that integrates a variational autoencoder (VAE) with a two-dimensional time-varying model predictive controller (MPC). In our primary simulation, compared with the proportional integral derivative (PID), MPC results in improvements by reducing the convergence time by 50%, lowering deformation error by 75%, producing smoother control inputs, and consuming one-sixth the energy. Moreover, MPC demonstrates strong adaptability, stability, and high precision in dynamic operating conditions, thereby ensuring surgical safety, particularly when subjected to discrete external forces. To reduce the computational load in real-time optimization, the VAE is trained offline using MPC data, and subsequently generates the optimal control sequences while enhancing interpretability. The proposed VAE-enhanced soft-robot deformation controller, termed VAI-SDC, can achieve approximately 17% greater energy savings and higher control accuracy than standalone MPC. The experimental results demonstrate that VAI-SDC can attain precise, energy-efficient deformation control of surgical instruments in time-varying environments. As the utilization of VAI-SDC minimizes the invasiveness of surgery, it promises reliable robotic assistance for the safety of clinical applications.