Mental-illness stigma is a persistent social problem, hampering both treatment-seeking and recovery. Accordingly, there is a pressing need to understand it more clearly, but analyzing the relevant data is highly labor-intensive. Therefore, we designed a chatbot to engage participants in conversations; coded those conversations qualitatively with AI assistance; and, based on those coding results, built causal knowledge graphs to decode stigma. The results we obtained from 1,002 participants demonstrate that conversation with our chatbot can elicit rich information about people's attitudes toward depression, while our AI-assisted coding was strongly consistent with human-expert coding. Our novel approach combining large language models (LLMs) and causal knowledge graphs uncovered patterns in individual responses and illustrated the interrelationships of psychological constructs in the dataset as a whole. The paper also discusses these findings' implications for HCI researchers in developing digital interventions, decomposing human psychological constructs, and fostering inclusive attitudes.