Multiplex networks have attracted more and more attention because they can model the coupling of network nodes between layers more accurately. The interaction of nodes between layers makes the attack effect on multiplex networks not simply a linear superposition of the attack effect on single-layer networks, and the disintegration of multiplex networks has become a research hotspot and difficult. Traditional multiplex network disintegration methods generally adopt approximate and heuristic strategies. However, these two methods have a number of drawbacks and fail to meet our requirements in terms of effectiveness and timeliness. In this paper, we develop a novel deep learning framework, called MINER (Multiplex network disintegration strategy Inference based on deep NEtwork Representation learning), which transforms the disintegration strategy inference of multiplex networks into the encoding and decoding process based on deep network representation learning. In the encoding process, the attention mechanism encodes the coupling relationship of corresponding nodes between layers, and reinforcement learning is adopted to evaluate the disintegration action in the decoding process. Experiments indicate that the trained MINER model can be directly transferred and applied to the disintegration of multiplex networks with different scales. We extend it to scenarios that consider node attack cost constraints and also achieve excellent performance. This framework provides a new way to understand and employ multiplex networks.