The growing Machine Learning (ML) services require extensive collections of user data, which may inadvertently include people's private information irrelevant to the services. Various studies have been proposed to protect private attributes by removing them from the data while maintaining the utilities of the data for downstream tasks. Nevertheless, as we theoretically and empirically show in the paper, these methods reveal severe vulnerability because of a common weakness rooted in their adversarial training based strategies. To overcome this limitation, we propose a novel approach, PASS, designed to stochastically substitute the original sample with another one according to certain probabilities, which is trained with a novel loss function soundly derived from information-theoretic objective defined for utility-preserving private attributes protection. The comprehensive evaluation of PASS on various datasets of different modalities, including facial images, human activity sensory signals, and voice recording datasets, substantiates PASS's effectiveness and generalizability.