Music rearrangement involves reshuffling, deleting, and repeating sections of a music piece with the goal of producing a standalone version that has a different duration. It is a creative and time-consuming task commonly performed by an expert music engineer. In this paper, we propose a method for automatically rearranging music recordings that takes into account the hierarchical structure of the recording. Previous approaches focus solely on identifying cut-points in the audio that could result in smooth transitions. We instead utilize deep audio representations to hierarchically segment the piece and define a cut-point search subject to the boundaries and musical functions of the segments. We score suitable entry- and exit-point pairs based on their similarity and the segments they belong to, and define an optimal path search. Experimental results demonstrate the selected cut-points are most commonly imperceptible by listeners and result in more consistent musical development with less distracting repetitions.