There are two issues in news-driven multi-stock movement prediction tasks that are not well solved in the existing works. On the one hand, the ``relation discovery'' is a pivotal part when leveraging the price information of other stocks to achieve accurate stock movement prediction. Considering that the stock relations are often unidirectional, such as the “supplier-consumer” relation, the causal relations are more appropriate to depict the impact between stocks. On the other hand, there are substantial noises existing in the news data leading to extracting effective information with difficulty. With these two issues into consideration, we propose a novel framework called CausalStock for news-driven multi-stock movement prediction, which discovers the temporal causal relations between stocks simultaneously. We design a lag-dependent temporal causal discovery mechanism to model the temporal causal graph distribution. Then Functional Causal Model is employed to encapsulate the discovered causal relations and predict the stock movements. Besides, we propose a Denoised News Encoder by taking advantage of the excellent text evaluation ability of large language models (LLMs) to pick up useful information from massive news data. The experiment results show that CausalStock exceeds the strong baselines for both news-driven multi-stock movement prediction and multi-stock movement prediction tasks on six real-world datasets collected from the US, China, Japan, and UK markets. Moreover, getting benefit from the causal relations, CausalStock could offer a clear prediction mechanism with good explainability.