Large-scale vision-language models (VLMs) have demonstrated remarkable versatility across a wide range of multimodal tasks. However, understanding humor remains challenging because humorous content often depends on subtle interactions among entities, events, context, and implicit relationships across image and text modalities. These interactions can involve complex chains of reasoning that are difficult to capture through conventional prompting or linear chain-of-thought reasoning. In this work, we propose CaRGo-T (Causal Reasoning Graph-of-Thought), a reasoning framework that represents the causal and contextual relationships underlying multimodal humor as a lightweight graph-based reasoning structure. The graph is serialized into a code-based representation generated by a VLM, which can subsequently be interpreted by the same or a different VLM to produce the final prediction in zero-shot or in-context learning settings. We evaluate CaRGo-T on humor understanding and humor detection across four datasets spanning diverse forms of comedic content, including satire, sarcasm, and memes. Experiments with state-of-the-art commercial and open-source VLMs show that CaRGo-T consistently improves performance over existing reasoning-based baselines, achieving gains of approximately 1-20% on humor understanding and 1-3% on humor detection. Further analysis using mutual information indicates that the reasoning representations produced by CaRGo-T contain more information relevant to the target output than those generated by baseline reasoning approaches. Code is available at https://github.com/abhi1nandy2/CaRGo-T.