Several face de-identification methods have been proposed to preserve users' privacy by obscuring their faces. These methods, however, can degrade the quality of photos, and they usually do not preserve the utility of faces, e.g., their age, gender, pose, and facial expression. Recently, advanced generative adversarial network models, such as StyleGAN, have been proposed, which generate realistic, high-quality imaginary faces. In this paper, we investigate the use of StyleGAN in generating de-identified faces through style mixing, where the styles or features of the target face and an auxiliary face get mixed to generate a de-identified face that carries the utilities of the target face. We examined this de-identification method with respect to preserving utility and privacy, by implementing several face detection, verification, and identification attacks. Through extensive experiments and also comparing with two state-of-the-art face de-identification methods, we show that StyleGAN preserves the quality and utility of the faces much better than the other approaches and also by choosing the style mixing levels correctly, it can preserve the privacy of the faces much better than other methods.