The rapid evolution of Text-to-Video (T2V) diffusion models has driven remarkable advancements in generating high-quality, temporally coherent videos from natural language descriptions. Despite these achievements, their vulnerability to adversarial attacks remains largely unexplored. In this paper, we introduce T2VAttack, a comprehensive study of adversarial attacks on T2V diffusion models from both semantic and temporal perspectives. Considering the inherently dynamic nature of video data, we propose two distinct attack objectives: a semantic objective to evaluate video-text alignment and a temporal objective to assess the temporal dynamics. To achieve an effective and efficient attack process, we propose two adversarial attack methods: (i) T2VAttack-S, which identifies semantically or temporally critical words in prompts and replaces them with synonyms via greedy search, and (ii) T2VAttack-I, which iteratively inserts optimized words with minimal perturbation to the prompt. By combining these objectives and strategies, we conduct a comprehensive evaluation on the adversarial robustness of several state-of-the-art T2V models, including ModelScope, CogVideoX, Open-Sora, and HunyuanVideo. Our experiments reveal that even minor prompt modifications, such as the substitution or insertion of a single word, can cause substantial degradation in semantic fidelity and temporal dynamics, highlighting critical vulnerabilities in current T2V diffusion models.