This study sheds light on the imperative need to bolster safety and privacy measures in large language models (LLMs), such as GPT-4 and LLaMA-2, by identifying and mitigating their vulnerabilities through explainable analysis of prompt attacks. We propose Counterfactual Explainable Incremental Prompt Attack (CEIPA), a novel technique where we guide prompts in a specific manner to quantitatively measure attack effectiveness and explore the embedded defense mechanisms in these models. Our approach is distinctive for its capacity to elucidate the reasons behind the generation of harmful responses by LLMs through an incremental counterfactual methodology. By organizing the prompt modification process into four incremental levels: (word, sentence, character, and a combination of character and word) we facilitate a thorough examination of the susceptibilities inherent to LLMs. The findings from our study not only provide counterfactual explanation insight but also demonstrate that our framework significantly enhances the effectiveness of attack prompts.