While the capabilities of generative foundational models have advanced rapidly in recent years, methods to prevent harmful and unsafe behaviors remain underdeveloped. Among the pressing challenges in AI safety, machine unlearning (MU) has become increasingly critical to meet upcoming safety regulations. Most existing MU approaches focus on altering the most significant parameters of the model. However, these methods often require fine-tuning substantial portions of the model, resulting in high computational costs and training instabilities, which are typically mitigated by access to the original training dataset. In this work, we address these limitations by leveraging Singular Value Decomposition (SVD) to create a compact, low-dimensional projection that enables the selective forgetting of specific data points. We propose Singular Value Decomposition for Efficient Machine Unlearning (SEMU), a novel approach designed to optimize MU in two key aspects. First, SEMU minimizes the number of model parameters that need to be modified, effectively removing unwanted knowledge while making only minimal changes to the model's weights. Second, SEMU eliminates the dependency on the original training dataset, preserving the model's previously acquired knowledge without additional data requirements. Extensive experiments demonstrate that SEMU achieves competitive performance while significantly improving efficiency in terms of both data usage and the number of modified parameters.