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Privacy concerns in the digital era highlight the sensitivity of facial images, revealing personal information beyond the identity. The current face deidentification techniques aiming to solve the issue often suffer from limitations. They either focus on narrow facial areas, compromise the image naturalness, lack flexibility in privacy levels, or offer suboptimal tradeoffs between the identity protection, image quality, and utility preservation. The paper presents a novel controllable face deidentification method that leverages StyleGAN2 and auxiliary classification approaches addressing these shortcomings. Validated across four datasets and compared to seven competitors, the method ensures a significant identity protection, preserves the data utility, maintains the diversity among deidentified faces, and demonstrates a promising performance. [ABSTRACT FROM AUTHOR]