Network pruning has become the de facto tool to accelerate deep neural networks for mobile and edge applications. Recently, feature-map discriminant based channel pruning has shown promising results, as it aligns well with the CNN's objective of differentiating multiple classes and offers better interpretability of the pruning decision. However, existing discriminant-based methods are challenged by computation inefficiency, as there is a lack of theoretical guidance on quantifying the feature-map discriminant power. In this paper, we develop a mathematical formulation to accurately and efficiently quantify the feature-map discriminativeness, which gives rise to a novel criterion, Discriminant Information (DI). We analyze the theoretical property of DI, specifically the non-decreasing property, that makes DI a valid channel selection criterion. By measuring the differential discriminant, we can identify and remove those channels with minimum influence to the discriminant power. The versatility of DI criterion also enables an intra-layer mixed precision quantization to further compress the network. Moreover, we propose a DI-based greedy pruning algorithm and structure distillation technique to automatically decide the pruned structure that satisfies certain resource budget, which is a common requirement in reality. Extensive experiments demonstrate the effectiveness of our method: our pruned ResNet50 on ImageNet achieves 44% FLOPs reduction without any Top-1 accuracy loss compared to unpruned model.