In the era of big data and the Internet of Things (IoT), data owners need to share a large amount of data with the intended receivers in an insecure environment, posing a trade-off issue between user privacy and data utility. The privacy utility trade-off was facilitated through a privacy funnel based on mutual information. Nevertheless, it is challenging to characterize the mutual information accurately with small sample size or unknown distribution functions. In this article, we propose a privacy funnel based on mutual information neural estimator (MINE) to optimize the privacy utility trade-off by estimating mutual information. Instead of computing mutual information in traditional way, we estimate it using an MINE, which obtains the estimated mutual information in a trained way, ensuring that the estimation results are as precise as possible. We employ estimated mutual information as a measure of privacy and utility, and then form a problem to optimize data utility by training a neural network while the estimator's privacy discourse is less than a threshold. The simulation results also demonstrated that the estimated mutual information from MINE works very well to approximate the mutual information even with a limited number of samples to quantify privacy leakage and data utility retention, as well as optimize the privacy utility trade-off.