Microfluidic-based separation methods have been highlighted for a number of biological applications, such as single cell analysis, disease diagnostics, and therapeutics. Although a number of previous studies have been carried out to minimize the physical damage and chemical deformations of the sample during the separation process, it still remains a challenge. In this paper, we developed a microfluidic device with dual-neodymium magnet-based negative magnetophoresis for the separation of the microparticles and cells. The poly(ethylene oxide) (PEO) was added to the solution to increase the viscoelasticity of the medium which could assist the sorting of the microparticles in the microfluidic device even at low flow rates, while minimizing damage to the cells and microparticles. Following this method, it was possible to separate 10 and 16 μm microparticles with high efficiency of 99 ± 0.1%, and 97 ± 0.8%, respectively. We also demonstrated the separation of glioblastoma cancer cells and neural stem cells (NSCs) in the microfluidic device.