Software architectures are usually meticulously designed to address multiple quality concerns and support long-term maintenance. However, there may be a lack of motivation for developers to document design rationales (i.e., the design alternatives and the underlying arguments for making or rejecting decisions) when they will not gain immediate benefit, resulting in a lack of standard capture of these rationales. With the turnover of developers, the architecture inevitably becomes eroded. This issue has motivated a number of studies to extract design knowledge from open-source communities in recent years. Unfortunately, none of the existing research has successfully extracted solutions alone with their corresponding arguments due to challenges such as the intricate semantics of online discussions and the lack of benchmarks for design rationale extraction. In this paper, we propose a novel approach, named DRMiner, to automatically mine latent design rationales from developers’ live discussion in open-source community (i.e., issue logs in Jira). To better identify solutions and their relevant arguments, DRMiner skillfully decomposes the problem into multiple text classification tasks and tackles them using prompt tuning of large language models (LLMs) and specific heuristic features. To evaluate DRMiner, we acquire issue logs from Cassandra, Flink, and Solr repositories in Jira and form a dataset for design rationale mining. Experimental results show that DRMiner outperforms all baselines and achieves F1 improvements of 24%, 22%, and 20% for mining design rationales, solutions, and arguments, respectively, compared to the best baseline. Furthermore, we investigate the usefulness of the design rationales mined by DRMiner for automated program repair (APR) and find that advanced LLMs, when prompted with these extracted rationales, generate 10x-18x more full-match patches and achieve a 10%-13% gain in CodeBLEU scores.