Community-based fact-checking is a promising approach to verify social media content and correct misleading posts at scale. Yet, causal evidence regarding its effectiveness in reducing the spread of misinformation on social media is missing. Here, we performed a large-scale empirical study to analyze whether community notes reduce the spread of misleading posts on X. Using a Difference-in-Differences design and repost time series data for N=237,677 (community fact-checked) cascades that had been reposted more than 431 million times, we found that exposing users to community notes reduced the spread of misleading posts by, on average, 62.0%. Furthermore, community notes increased the odds that users delete their misleading posts by 103.4%. However, our findings also suggest that community notes might be too slow to intervene in the early (and most viral) stage of the diffusion. Our work offers important implications to enhance the effectiveness of community-based fact-checking approaches on social media.