While suction-cast ZrCu-based bulk metallic glasses show combinations of high strength and fracture toughness, the same alloy processed using laser additive manufacturing suffers from a strongly reduced damage tolerance. Through a range of advanced analytical techniques and mechanical measurements from macro to micro length-scales, the reduced damage tolerance of the laser-processed material was found to be linked to the insertion of oxygen within the short- and medium range ordering of the glass. Further, the interaction of atomic-scale structural ordering and strain rate in affecting the deformation response of ZrCu-based glass micropillars were studied by varying the concentration of oxygen dissolved into the local structure of a suction-cast alloy. A pair distribution function analysis from high-energy X-ray microdiffraction experiments confirmed the effects of oxygen on the atomic-scale structural order. Compression of micropillars over six decades of strain rate (5 × 10^-4 to 5 × 10² s^-1) uncovered a remarkable reversal of the strain rate sensitivity from negative to positive above ~5 s^-1 due to a delocalisation of shear transformation events within the pre-yield linear regime for both samples, while a higher oxygen content was found to generally decrease the strain rate sensitivity effect. Based on micromechanical measurements, this work highlights the importance of shear transformation zone activation of metallic glasses within the elastic limit.