Environmental experts have developed the DPSIR (Driver, Pressure, State, Impact, Response) framework to systematically study and communicate key relationships between society and the environment. Using this framework requires experts to construct a DPSIR taxonomy from a corpus, annotate the documents, and identify DPSIR variables and relationships, which is laborious and inflexible. Automating it with conventional text mining faces technical challenges, primarily because the taxonomy often begins with abstract definitions, which experts progressively refine and contextualize as they annotate the corpus. In response, we develop GreenMine, a system that supports interactive text mining with prompt engineering. The system implements a prompting pipeline consisting of three simple and evaluable subtasks. In each subtask, the DPSIR taxonomy can be defined in natural language and iteratively refined as experts analyze the corpus. To support users evaluate the taxonomy, we introduce an uncertainty score based on response consistency. Then, we design a radial uncertainty chart that visualizes uncertainties and corpus topics, which supports interleaved evaluation and exploration. Using the system, experts can progressively construct the DPSIR taxonomy and annotate the corpus with LLMs. Using real-world interview transcripts, we present a case study to demonstrate the capability of the system in supporting interactive mining of DPSIR relationships, and an expert review in the form of collaborative discussion to understand the potential and limitations of the system. We discuss the lessons learned from developing the system and future opportunities for supporting interactive text mining in knowledge-intensive tasks for other application scenarios.