Convolutional Neural Networks (CNNs) are commonly designed for closed set arrangements, where test instances only belong to some "Known Known" (KK) classes used in training. As such, they predict a class label for a test sample based on the distribution of the KK classes. However, when used under the Open Set Recognition (OSR) setup (where an input may belong to an "Unknown Unknown" or UU class), such a network will always classify a test instance as one of the KK classes even if it is from a UU class. As a solution, recently, data augmentation based on Generative Adversarial Networks(GAN) has been used. In this work, we propose a novel approach for mining a "Known UnknownTrainer" or KUT set and design a deep OSR Network (OSRNet) to harness this dataset. The goal isto teach OSRNet the essence of the UUs through KUT set, which is effectively a collection of mined "hard Known Unknown negatives". Once trained, OSRNet can detect the UUs while maintaining high classification accuracy on KKs. We evaluate OSRNet on six benchmark datasets and demonstrate it outperforms contemporary OSR methods.