We have investigated the laser micromachining of microsieves with 3D micropore geometries. We hypothesize that mechanical cues resulting from the positioning and machining of ablated holes inside a pyramidal microcavity can influence the direction of neuronal outgrowth and instruct stem cell-derived neural networks in their differentiation processes. We narrowed the number of variations in device fabrication by developing a numerical model to estimate the stress distribution in a cell interacting with the laser-tailored unique 3D geometry of a microsieve’s pore. Our model is composed of two components: a continuous component (consisting of the membrane, cytoplasm, and nucleus) and a tensegrity structural component (consisting of the cytoskeleton, nucleoskeleton, and intermediate filaments). The final values of the mechanical properties of the components are selected after evaluating the shape of the continuous cell model when a gravity load is applied and are compared to the shape of a cell on a glass substrate after 3 h. In addition, a physical criterion implying that the cell should not slip through a hole with a bottom aperture of 3.5  μm is also set as a constraint. Among all the possible one- or multi-hole configurations, six cases appeared promising in influencing the polarization process of the cell. These configurations were selected, fabricated, and characterized using scanning electron microscopy. Fabricated microsieves consist of a 20  μm thick Norland Optical Adhesive 81 (NOA81) foil with an array of inverted pyramidal microcavities, which are opened by means of KrF 248 nm laser ablation. By changing the position of the laser beam spot on the cavities (center, slope, or corner) as well as the direction of laser beam with respect to the NOA81 microcavity foil (top side or back side), different ablation configurations yielded a variety of geometries of the 3D micropores. In the one-hole configurations when the shot is from the top side, to make the desired diameter of 3.5  μm (or less) of an opening, 1500 laser pulses are sufficient for the center and slope openings. This requirement is around 2000 laser pulses when the aperture is positioned in the corner. In back side ablation processes, the required number of pulses for through-holes at the center, slope, and corner positions are 1200, 1800, and 1800 pulses, respectively. In conclusion, we developed a microsieve platform that allows us to tailor the 3D topography of individual micropores according to the selection of cases guided by our numerical stress distribution models.