Zero-shot Spoken Language Understanding (SLU) aims to enable task-oriented dialogue systems to understand user needs without training data. Challenging but worthwhile, zero-shot SLU reduces the time and effort that data labeling takes. Recent advancements in large language models (LLMs), such as GPT3.5 and ChatGPT, have shown promising results in zero-shot settings, which motivates us to explore prompt-based methods. In this study, we investigate whether strong SLU models can be constructed by directly prompting LLMs. Specifically, we propose a simple yet effective two-stage framework dubbed GPT-SLU, which transforms the SLU task into a question-answering problem. Powered by multi-stage mutual guided prompts, GPT-SLU can leverage the correlations between two subtasks in SLU to achieve better predictions, which is greatly explored in the traditional fine-tuning paradigm. Experimental results on three SLU benchmark datasets demonstrate the significant potential of LLMs for zero-shot SLU. Comprehensive analyses validate the effectiveness of our proposed framework and also indicate that there is still room for further improvement of LLMs in SLU scenarios.