Metal-organic framework (MOF) glasses provide new perspectives on many material properties due to their unique chemical and structural nature. Their mechanical properties are of particular interest because glasses are inherently brittle, which limits their applications as structural materials. Here we perform strain-rate-dependent uniaxial micropillar compression experiments on agZIF-62, agZIF-UC-5, and agTIF-4, a series of MOF glasses with different substituting linker molecules, and find that these glasses show substantial plasticity, at least on the micrometer scale. At a quasi-static strain rate of 0.001 s-1, the micropillars yielded at approximately 0.32 GPa and subsequently deformed plastically up to 35% strain, irrespective of the type of substituting linker. With increasing strain rate, the yield strength of agZIF-62 evolved with the strain-rate sensitivity m = 0.024 to reach a yield strength of 0.44 GPa at a strain rate of 510 s-1. On the basis of this relatively low strain-rate sensitivity and the absence of serrated flow, we conclude that structural densification is the predominant mechanism that accommodates such extensive plasticity.