The electroencephalogram (EEG) has recently emerged as a pivotal tool in brain imaging analysis, playing a crucial role in accurately interpreting brain functions and states. To address the problem that the presence of ocular artifacts in the EEG signals of patients with obstructive sleep apnea syndrome (OSAS) severely affects the accuracy of sleep staging recognition, we propose a method that integrates a support vector machine (SVM) with genetic algorithm (GA)-optimized variational mode decomposition (VMD) and second-order blind identification (SOBI) for the removal of ocular artifacts from single-channel EEG signals. The SVM is utilized to identify artifact-contaminated segments within preprocessed single-channel EEG signals. Subsequently, these signals are decomposed into variational modal components across different frequency bands using the GA-optimized VMD algorithm. These components undergo further decomposition via the SOBI algorithm, followed by the computation of their approximate entropy. An approximate entropy threshold is set to identify and remove components laden with ocular artifacts. Finally, the signal is reconstructed using the inverse SOBI and VMD algorithms. To validate the efficacy of our proposed method, we conducted experiments utilizing both simulated data and real OSAS sleep EEG data. The experimental results demonstrate that our algorithm not only effectively mitigates the presence of ocular artifacts but also minimizes EEG signal distortion, thereby enhancing the precision of sleep staging recognition based on the EEG signals of OSAS patients.