Quantum transport in disordered systems poses intriguing fundamental questions, such as the interplay of disorder, interactions, and decoherence, and has attracted significant interest. These fundamental aspects also have important implications in real-world scenarios, such as energy transfer in nanoscale systems (e.g. light harvesting complexes) and quantum information transfer. This large body of work spanning broad research areas in Physics, Chemistry and Nanotechnology has led to major insights and advances, yet open questions remain, namely in terms of the emergence of multiple timescales observed in the dynamics of such systems. Here, we investigate the emergence of multiple transport timescales in the dissipative dynamics of a spin impurity coupled to a small, spatially disordered network of spins. Using a two-dimensional tight-binding model with dipolar interactions and local dephasing, we demonstrate that geometric heterogeneity leads to hierarchical coupling strengths. This results in pronounced separation of dynamical timescales, far beyond those expected in homogeneous environments. By analyzing different metrics for dynamics, we identify distinct relaxation timescales associated with cluster-level equilibration and global equilibration. A minimal three-site model reveals the physical origin of the longest timescale: strong internal hybridization internally generates an effective detuning that suppresses transfer to other weakly-coupled sites, yielding a parametrically-enhanced relaxation time in the weak-dephasing regime. We corroborate this picture with nonequilibrium steady-state transport calculations and extensive simulations of disordered spin configurations, demonstrating orders-of-magnitude slowing of relaxation when hierarchical couplings are present. Our results highlight the central role of geometry and connectivity in spin networks and open quantum systems in general, and provide experimentally relevant predictions for relaxation times in small spin baths.