Emerging Large Reasoning Models (LRMs) consistently excel in mathematical and reasoning tasks, showcasing exceptional capabilities. However, the enhancement of reasoning abilities and the exposure of their internal reasoning processes introduce new safety vulnerabilities. One intriguing concern is: when reasoning is strongly entangled with harmfulness, what safety-reasoning trade-off do LRMs exhibit? To address this issue, we introduce HauntAttack, a novel and general-purpose black-box attack framework that systematically embeds harmful instructions into reasoning questions. Specifically, we treat reasoning questions as carriers and substitute one of their original conditions with a harmful instruction. This process creates a reasoning pathway in which the model is guided step by step toward generating unsafe outputs. Based on HauntAttack, we conduct comprehensive experiments on multiple LRMs. Our results reveal that even the most advanced LRMs exhibit significant safety vulnerabilities. Additionally, we perform a detailed analysis of different models, various types of harmful instructions, and model output patterns, providing valuable insights into the security of LRMs.