In this work, we explore the task of hierarchical distance-based speech separation defined on a hyperbolic manifold. Based on the recent advent of audio-related tasks performed in non-Euclidean spaces, we propose to make use of the Poincaré ball to effectively unveil the inherent hierarchical structure found in complex speaker mixtures. We design two sets of experiments in which the distance-based parent sound classes, namely "near" and "far", can contain up to two or three speakers (i.e., children) each. We show that our hyperbolic approach is suitable for unveiling hierarchical structure from the problem definition, resulting in improved child-level separation. We further show that a clear correlation emerges between the notion of hyperbolic certainty (i.e., the distance to the ball's origin) and acoustic semantics such as speaker density, inter-source location, and microphone-to-speaker distance.