Surgical robot task automation has been a promising research topic for improving surgical efficiency and quality. Learning-based methods have been recognized as an interesting paradigm and been increasingly investigated. However, existing approaches encounter difficulties in long-horizon goal-conditioned tasks due to the intricate compositional structure, which requires decision-making for a sequence of sub-steps and understanding of inherent dynamics of goal-reaching tasks. In this paper, we propose a new learning-based framework by leveraging the strong reasoning capability of the GPT-based architecture to automate surgical robotic tasks. The key to our approach is developing a goal-conditioned decision transformer to achieve sequential representations with goal-aware future indicators in order to enhance temporal reasoning. Moreover, considering to exploit a general understanding of dynamics inherent in manipulations, thus making the model's reasoning ability to be task-agnostic, we also design a cross-task pretraining paradigm that uses multiple training objectives associated with data from diverse tasks. We have conducted extensive experiments on 10 tasks using the surgical robot learning simulator SurRoL~\cite{long2023human}. The results show that our new approach achieves promising performance and task versatility compared to existing methods. The learned trajectories can be deployed on the da Vinci Research Kit (dVRK) for validating its practicality in real surgical robot settings. Our project website is at: https://med-air.github.io/SurRoL.