Micro-deep drawing (MDD) is a promising micro-manufacturing technology. Size effects complicate and signify the influence of the blank holder-die gap on MDD, which was investigated in this study. Annealing of SUS304 foils of 50 µm thick was conducted to obtain various grain sizes. Micro-tensile testing was carried out to acquire the stress-strain curves of the foils, followed by MDD experiments. Advanced FE models were developed to simulate the MDD process taking into account material inhomogeneity and surface morphology of the foils at micro-scale. Bending dominates the early stage of MDD. A combination of proper gap size and punch/die corner radius may incur in-process springback before the occurrence of the maximum drawing force, benefiting the MDD process. A relatively small gap is favourable to a uniform distribution of wall thickness without obviously increasing the risk of fracture. It also improves the overall shape accuracy of outer surface whilst may result in the inner surface distortion. The complex development of the shape accuracy in three defined areas on the drawn cup can be attributed to the integrated effect of the gap size, material inhomogeneity and surface morphology of the foil. The combined design and multi-object optimisation of the gap size and the corner radii of punch and die should be conducted for improving the MDD process.