Recent years have witnessed the emerging success of leveraging syntax graphs for the target sentiment classification task. However, we discover that existing syntax-based models suffer from two issues: noisy information aggregation and loss of distant correlations. In this paper, we propose a novel model termed Neural Subgraph Explorer, which (1) reduces the noisy information via pruning target-irrelevant nodes on the syntax graph; (2) introduces beneficial first-order connections between the target and its related words into the obtained graph. Specifically, we design a multi-hop actions score estimator to evaluate the value of each word regarding the specific target. The discrete action sequence is sampled through Gumble-Softmax and then used for both of the syntax graph and the self-attention graph. To introduce the first-order connections between the target and its relevant words, the two pruned graphs are merged. Finally, graph convolution is conducted on the obtained unified graph to update the hidden states. And this process is stacked with multiple layers. To our knowledge, this is the first attempt of target-oriented syntax graph pruning in this task. Experimental results demonstrate the superiority of our model, which achieves new state-of-the-art performance.