Recent advancements in large language models (LLMs) have led to the development of highly potent models like OpenAI's ChatGPT. These models have exhibited exceptional performance in a variety of tasks, such as question answering, essay composition, and code generation. However, their effectiveness in the healthcare sector remains uncertain. In this study, we seek to investigate the potential of LLMs to aid in clinical text mining by examining their ability to extract structured information from unstructured healthcare texts, with a focus on biological named entity recognition and relation extraction. However, our preliminary results indicate that employing LLMs directly for these tasks resulted in poor performance and raised privacy concerns associated with uploading patients' information to the LLM API. To overcome these limitations, we propose a new training paradigm that involves generating a vast quantity of high-quality synthetic data with labels utilizing LLMs and fine-tuning a local model for the downstream task. Our method has resulted in significant improvements in the performance of downstream tasks, improving the F1-score from 23.37% to 63.99% for the named entity recognition task and from 75.86% to 83.59% for the relation extraction task. Furthermore, generating data using LLMs can significantly reduce the time and effort required for data collection and labeling, as well as mitigate data privacy concerns. In summary, the proposed framework presents a promising solution to enhance the applicability of LLM models to clinical text mining.