Visual question answering (VQA) can be fundamentally crucial for promoting robotic-assisted surgical education. In practice, the needs of trainees are constantly evolving, such as learning more surgical types, adapting to different robots, and learning new surgical instruments and techniques for one surgery. Therefore, continually updating the VQA system by a sequential data stream from multiple resources is demanded in robotic surgery to address new tasks. In surgical scenarios, the storage cost and patient data privacy often restrict the availability of old data when updating the model, necessitating an exemplar-free continual learning (CL) setup. However, prior studies overlooked two vital problems of the surgical domain: i) large domain shifts from diverse surgical operations collected from multiple departments or clinical centers, and ii) severe data imbalance arising from the uneven presence of surgical instruments or activities during surgical procedures. This paper proposes to address these two problems with a multimodal large language model (LLM) and an adaptive weight assignment methodology. We first develop a new multi-teacher CL framework that leverages a multimodal LLM as the additional teacher. The strong generalization ability of the LLM can bridge the knowledge gap when domain shifts and data imbalances occur. We then put forth a novel data processing method that transforms complex LLM embeddings into logits compatible with our CL framework. We further design an adaptive weight assignment approach that balances the generalization ability of the LLM and the domain expertise of the old CL model. We construct a new dataset for surgical VQA tasks, providing valuable data resources for future research. Extensive experimental results on three datasets demonstrate the superiority of our method to other advanced CL models.