Instruction-following large language models (LLMs), such as ChatGPT, have become increasingly popular with the general audience, many of whom are incorporating them into their daily routines. However, these LLMs inadvertently disclose personal or copyrighted information, which calls for a machine unlearning method to remove selective knowledge. Previous attempts sought to forget the link between the target information and its associated entities, but it rather led to generating undesirable responses about the target, compromising the end-user experience. In this work, we propose SNAP, an innovative framework designed to selectively unlearn information by 1) training an LLM with negative instructions to generate obliterated responses, 2) augmenting hard positives to retain the original LLM performance, and 3) applying the novel Wasserstein regularization to ensure adequate deviation from the initial weights of the LLM. We evaluate our framework on various NLP benchmarks and demonstrate that our approach retains the original LLM capabilities, while successfully unlearning the specified information.