In healthcare, portable EEG machines are widely used for recording and analyzing brain signals due to their ease of use and affordability. However, these devices often face challenges with EOG artifacts, which are large, low-frequency signals caused by eye blinks. This interference can compromise accurate diagnosis. As a result, there is a significant need for improved methods to remove these artifacts in single-channel portable EEG devices to ensure reliable analysis and diagnosis. In this work, a hybrid framework combining the Empirical Wavelet Transform (EWT) and Savitzky-Golay (SG) filter is proposed. This approach effectively detects EOG artifacts in contaminated signals and removes them while preserving the integrity of the EEG content. The method achieves strong performance metrics, such as a correlation coefficient (CC) of 0.96, a mean absolute error (MAE) of 0.27 at 0 dB, and a signal-to-artifact ratio (SAR) of 1.12. The proposed method has been evaluated on both synthetic and real EEG datasets. When compared to existing techniques, it demonstrates superior performance across the evaluated metrics, highlighting its effectiveness and reliability.