As the Internet and social media evolve rapidly, distinguishing credible news from a vast amount of complex information poses a significant challenge. Due to the suddenness and instability of news events, the authenticity labels of news can potentially shift as events develop, making it crucial for fake news detection to obtain the latest event updates. Existing methods employ retrieval-augmented generation to fill knowledge gaps, but they suffer from issues such as insufficient credibility of retrieved content and interference from noisy information. We propose a dynamic knowledge update-driven model for fake news detection (DYNAMO), which leverages knowledge graphs to achieve continuous updating of new knowledge and integrates with large language models to fulfill dual functions: news authenticity detection and verification of new knowledge correctness, solving the two key problems of ensuring the authenticity of new knowledge and deeply mining news semantics. Specifically, we first construct a news-domain-specific knowledge graph. Then, we use Monte Carlo Tree Search to decompose complex news and verify them step by step. Finally, we extract and update new knowledge from verified real news texts and reasoning paths. Experimental results demonstrate that DYNAMO achieves the best performance on two real-world datasets.