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Program slicing has been widely applied in a variety of software engineering tasks. However, existing program slicing techniques only deal with traditional programs that are constructed with instructions and variables, rather than neural networks that are composed of neurons and synapses. In this paper, we propose NNSlicer, the first approach for slicing deep neural networks based on data flow analysis. Our method understands the reaction of each neuron to an input based on the difference between its behavior activated by the input and the average behavior over the whole dataset. Then we quantify the neuron contributions to the slicing criterion by recursively backtracking from the output neurons, and calculate the slice as the neurons and the synapses with larger contributions. We demonstrate the usefulness and effectiveness of NNSlicer with three applications, including adversarial input detection, model pruning, and selective model protection. In all applications, NNSlicer significantly outperforms other baselines that do not rely on data flow analysis.