Recent reasoning large language models (LLMs), such as OpenAI o1 and DeepSeek-R1, exhibit strong performance on complex tasks through test-time inference scaling. However, prior studies have shown that these models often incur significant computational costs due to excessive reasoning, such as frequent switching between reasoning trajectories (e.g., underthinking) or redundant reasoning on simple questions (e.g., overthinking). In this work, we expose a novel threat: adversarial inputs can be crafted to exploit excessive reasoning behaviors and substantially increase computational overhead without compromising model utility. Therefore, we propose a novel loss framework consisting of three components: (1) Priority Cross-Entropy Loss, a modification of the standard cross-entropy objective that emphasizes key tokens by leveraging the autoregressive nature of LMs; (2) Excessive Reasoning Loss, which encourages the model to initiate additional reasoning paths during inference; and (3) Delayed Termination Loss, which is designed to extend the reasoning process and defer the generation of final outputs. We optimize and evaluate our attack for the GSM8K and ORCA datasets on DeepSeek-R1-Distill-LLaMA and DeepSeek-R1-Distill-Qwen. Empirical results demonstrate a 3x to 9x increase in reasoning length with comparable utility performance. Furthermore, our crafted adversarial inputs exhibit transferability, inducing computational overhead in o3-mini, o1-mini, DeepSeek-R1, and QWQ models.