Owing to a lack of microstructure, glassy materials are inherently strong but brittle, and often demonstrate extreme sensitivity to flaws. Accordingly, their macroscopic failure is often not initiated by plastic yielding, and almost always terminated by brittle fracture. Unlike conventional brittle glasses, metallic glasses are generally capable of limited plastic yielding by shear-band sliding in the presence of a flaw, and thus exhibit toughness-strength relationships that lie between those of brittle ceramics and marginally tough metals. Here, a bulk glassy palladium alloy is introduced, demonstrating an unusual capacity for shielding an opening crack accommodated by an extensive shear-band sliding process, which promotes a fracture toughness comparable to those of the toughest materials known. This result demonstrates that the combination of toughness and strength (that is, damage tolerance) accessible to amorphous materials extends beyond the benchmark ranges established by the toughest and strongest materials known, thereby pushing the envelope of damage tolerance accessible to a structural metal.