Deformability of metallic glasses (MGs) is strongly influenced by their thermomechanical processing history that governs their energy state and local atomic configurations. Here, we reveal that monatomic tantalum MG nanowires, tailored by electropulsing, can attain a remarkable range of deformability, manifesting as either liquid-like flow or brittle fracture. Inherent structural heterogeneity on the level of atomic order dominates the plasticity and deformation transition of monatomic MGs. By tracking atomic rearrangement during straining, we find the dispersive and sparse distribution of local order is associated with necking, yet percolation of medium-range order constrains the deformability and results in brittle failure. This work sheds new light on the structure-property relationships in MGs, which has important implications for the design of nanoscale MGs with tunable mechanical properties.