Sarcasm detection is a crucial yet challenging Natural Language Processing task. Existing Large Language Model methods are often limited by single-perspective analysis, static reasoning pathways, and a susceptibility to hallucination when processing complex ironic rhetoric, which impacts their accuracy and reliability. To address these challenges, we propose SEVADE, an novel Self-Evolving multi-agent Analysis framework with Decoupled Evaluation for hallucination-resistant sarcasm detection. The core of our framework is a Dynamic Agentive Reasoning Engine (DARE), which utilizes a team of specialized agents grounded in linguistic theory to perform a multifaceted deconstruction of the text and generate a structured reasoning chain. Subsequently, a separate lightweight rationale adjudicator (RA) performs the final classification based solely on this reasoning chain. This decoupled architecture is designed to mitigate the risk of hallucination by separating complex reasoning from the final judgment. Extensive experiments on four benchmark datasets demonstrate that our framework achieves state-of-the-art performance, with average improvements of 6.75% in Accuracy and 6.29% in Macro-F1 score.