We present and evaluate Deep Private-Feature Extractor (DPFE), a deep model which is trained and evaluated based on information theoretic constraints. Using the selective exchange of information between a user's device and a service provider, DPFE enables the user to prevent certain sensitive information from being shared with a service provider, while allowing them to extract approved information using their model. We introduce and utilize the log-rank privacy, a novel measure to assess the effectiveness of DPFE in removing sensitive information and compare different models based on their accuracy-privacy trade-off. We then implement and evaluate the performance of DPFEon smartphones to understand its complexity, resource demands, and efficiency trade-offs. Our results on benchmark image datasets demonstrate that under moderate resource utilization, DPFE can achieve high accuracy for primary tasks while preserving the privacy of sensitive information.