In microfluidic filtration systems, one of the leading obstacles to efficient, continuous operation is clogging of the filters. Here, we introduce a lateral flow microfluidic sieving (μ-sieving) technique to overcome clogging and to allow continuous operation of filter based microfluidic separation. A low frequency mechanical oscillation was added to the fluid flow, which made possible the release of aggregated unwanted polystyrene (PS) particles trapped between the larger target PS particles in the filter demonstrating continuous μ-sieving operation. We achieved collection of the target PS particles with 100% separation efficiency. Also, on average, more than 98% of the filtered target particles were retrieved after the filtration showing high retrieval rates. Since the oscillation was applied to the fluid but not to the microfluidic filter system, mechanical stresses to the system was minimized and no additional fabrication procedures were necessary. We also applied the μ-sieving technique to the separation of cancer cells (MDA-MB-231) from whole blood and showed that the fluidic oscillations prevented the filters from being blocked by the filtered cancer cells allowing continuous microfluidic separation with high efficiency.