Intermediate filaments (IFs), in addition to microtubules and microfilaments, are one of the three major components of the cytoskeleton in eukaryotic cells, playing a vital role in mechanotransduction and in providing mechanical stability to cells. Despite the importance of IF mechanics for cell biology and cell mechanics, the structural basis for their mechanical properties remains unknown. Specifically, our understanding of fundamental filament properties, such as the basis for their great extensibility, stiffening properties, and their exceptional mechanical resilience remains limited. This has prevented us from answering fundamental structure-function relationship questions related to the biomechanical role of intermediate filaments, which is crucial to link structure and function in the protein material's biological context. Here we utilize an atomistic-level model of the human vimentin dimer and tetramer to study their response to mechanical tensile stress, and describe a detailed analysis of the mechanical properties and associated deformation mechanisms. We observe a transition from alpha-helices to beta-sheets with subsequent interdimer sliding under mechanical deformation, which has been inferred previously from experimental results. By upscaling our results we report, for the first time, a quantitative comparison to experimental results of IF nanomechanics, showing good agreement. Through the identification of links between structures and deformation mechanisms at distinct hierarchical levels, we show that the multi-scale structure of IFs is crucial for their characteristic mechanical properties, in particular their ability to undergo severe deformation of approximately 300% strain without breaking, facilitated by a cascaded activation of a distinct deformation mechanisms operating at different levels. This process enables IFs to combine disparate properties such as mechanosensitivity, strength and deformability. Our results enable a new paradigm in studying biological and mechanical properties of IFs from an atomistic perspective, and lay the foundation to understanding how properties of individual protein molecules can have profound effects at larger length-scales.