Mining a set of meaningful and distinctive topics automatically from massive text corpora has broad applications. Existing topic models, however, typically work in a purely unsupervised way, which often generate topics that do not fit users' particular needs and yield suboptimal performance on downstream tasks. We propose a new task, discriminative topic mining, which leverages a set of user-provided category names to mine discriminative topics from text corpora. This new task not only helps a user understand clearly and distinctively the topics he/she is most interested in, but also benefits directly keyword-driven classification tasks. We develop CatE, a novel category-name guided text embedding method for discriminative topic mining, which effectively leverages minimal user guidance to learn a discriminative embedding space and discover category representative terms in an iterative manner. We conduct a comprehensive set of experiments to show that CatE mines high-quality set of topics guided by category names only, and benefits a variety of downstream applications including weakly-supervised classification and lexical entailment direction identification.