There is a high demand for bespoke grafts to replace damaged or malformed bone and cartilage tissue. Three-dimensional (3D) printing offers a method of fabricating complex anatomical features of clinically relevant sizes. However, the construction of a scaffold to replicate the complex hierarchical structure of natural tissues remains challenging. This paper reports a novel biofabrication method that is capable of creating intricately designed structures of anatomically relevant dimensions. The beneficial properties of the electrospun fibre meshes can finally be realised in 3D rather than the current promising breakthroughs in two-dimensional (2D). The 3D model was created from commercially available computer-aided design software packages in order to slice the model down into many layers of slices, which were arrayed. These 2D slices with each layer of a defined pattern were laser cut, and then successfully assembled with varying thicknesses of 100 μm or 200 μm. It is demonstrated in this study that this new biofabrication technique can be used to reproduce very complex computer-aided design models into hierarchical constructs with micro and nano resolutions, where the clinically relevant sizes ranging from a simple cube of 20 mm dimension, to a more complex, 50 mm-tall human ears were created. In-vitro cell-contact studies were also carried out to investigate the biocompatibility of this hierarchal structure. The cell viability on a micromachined electrospun polylactic-co-glycolic acid fibre mesh slice, where a range of hole diameters from 200 μm to 500 μm were laser cut in an array where cell confluence values of at least 85% were found at three weeks. Cells were also seeded onto a simpler stacked construct, albeit made with micromachined poly fibre mesh, where cells can be found to migrate through the stack better with collagen as bioadhesives. This new method for biofabricating hierarchical constructs can be further developed for tissue repair applications such as maxillofacial bone injury or nose/ear cartilage replacement in the future.