Ionic liquids (ILs) are promising entrainers in the separation of azeotropic systems with unique advantages, such as environmental benignity and flexible design. In this work, we carried out molecular dynamics (MD) simulations to elucidate the underlying mechanism in the separation of a typical azeotropic mixture, acetone (A)-methanol (M), using an efficient IL entrainer, 1,3-dimethylimidazolium dimethylphosphate [MMIM][HDM]), which was proposed in our previous work. Upon the addition of the IL, the excess enthalpies decrease significantly, especially in the acetone-rich mixture. An analysis based on energy breakdown in MD simulations indicated that the interactions between methanol and [DMP](-) play a major role in the elimination of the azeotrope. In terms of the radial distribution function, spatial distribution function, and combined distribution function, we discussed the microscopic structures to clarify various interactions among the mixtures. It was found that various clusters of dimensions less than 10 angstrom are formed by methanol and [DMP](-), in the acetone- rich mixture upon the addition of the IL. In addition, we distinguished the types of these clusters in terms of their different connection modes by the detailed information extracted in simulations. Results indicated that the interplay of two kinds of hydrogen bonds, that is, O-H(M)center dot center dot center dot O2(D) and O-H(M)center dot center dot center dot O(M), is responsible for the formation of these clusters. We provided important information to understand the mechanisms of azeotrope elimination by the IL, which is valuable to design new entrainers in the future.