Online debates provide critical insights into public opinion and societal trends, yet the unstructured nature of these discussions presents significant challenges for analysis. In this paper, we present SAGESSE, a novel argumentation parsing pipeline tailored to Reddit debates, leveraging the capabilities of large language models to structure and interpret complex online arguments. SAGESSE generates detailed argument maps that organize debates systematically, offering a clearer understanding of discourse dynamics. We have developed a web application where users can select controversial Reddit topics and visualize the corresponding argument maps generated from user comments. This tool has the potential to aid analysts, policymakers, and researchers in tracking debate progress, gauging public sentiment, and identifying influential arguments. The web application is available at https://modemos.epfl.ch/sagesse/. CCS Concepts • Information systems → Language models.