Micromachined polymeric honeycomb membranes having conventional and re-entrant cell geometries have been fabricated using femtosecond laser ablation. Mechanical properties characterization confirms that the re-entrant membrane is auxetic (possesses negative Poisson＇s ratios: nu(xy) = -1.82 +/- 0.05 and nu(yx) = -0.51 +/- 0.01) whereas the conventional membrane possesses positive Poisson＇s ratios (nu(xy) = +0.86 +/- 0.06 and nu(yx) = +0.6 +/- 0.1). Comparison with honeycomb theory confirms that the dominant deformation mechanism is flexure of the honeycomb ribs. The auxetic membrane has been challenged with single-sized glass chromatography beads such that the beads were initially resting on the re-entrant cells. Subsequent tensile loading of the membrane showed the auxetic cells opening during deformation, enabling the beads to pass through the membrane. We have modeled the pare-opening properties of both types of membranes, and the observed behavior for the auxetic membrane is consistent with the model. This is a clear proof-of-concept demonstration of the potential of auxetic materials and structures in filter defouling or cleaning operations. This paper, therefore, demonstrates the successful design and fabrication of a micromachined auxetic structure having specifically tailored mechanical properties that show enhanced functional performance over the conventional filter structure.