Ba₂CuTeO₆ has attracted significant attention as it contains a two-leg spin ladder of Cu²⁺ cations that lies in close proximity to a quantum critical point. Recently, Ba₂CuTeO₆ has been shown to accommodate chemical substitutions, which can significantly tune its magnetic behavior. Here, we investigate the effects of substitution for non-magnetic Zn²⁺ impurities at the Cu²⁺ site, partitioning the spin ladders. Results from bulk thermodynamic and local muon magnetic characterization on the Ba₂Cu_1 – xZn_xTeO₆ solid solution (0 ≤ x ≤ 0.6) indicate that Zn²⁺ partitions the Cu²⁺ spin ladders into clusters and can be considered using the percolation theory. As the average cluster size decreases with increasing Zn²⁺ substitution, there is an evolving transition from long-range order to spin-freezing as the critical cluster size is reached between x = 0.1 to x = 0.2, beyond which the behavior became paramagnetic. This demonstrates well-controlled tuning of the magnetic disorder, which is highly topical across a range of low-dimensional Cu²⁺-based materials. However, in many of these cases, the chemical disorder is also relatively strong in contrast to Ba₂CuTeO₆ and its derivatives. Therefore, Ba₂Cu_1 – xZn_xTeO₆ provides an ideal model system for isolating the effect of defects and segmentation in low-dimensional quantum magnets.