The separation of particles such as cells and bacteria in viscoelastic fluids has significant applications in biomedical fields. At present, one of the main challenges that limit the application of microfluidic technology is to separate particles in the viscoelastic fluids with different rheological properties. For instance, most existing microfluidic devices can only work in the fluid with a specific rheological property, resulting in the requirement of time-consuming design, manufacturing, testing, and optimization of different devices to separate particles in the fluids with different rheological properties. In this work, a novel hybrid three-stage microfluidic device that was made up of a micropore structure and two gradually contracted microchannels was designed to achieve efficient continuous separation of particles in the viscoelastic fluid over a wide range of rheological properties (0.07 < El < 340.41). Different separation strategies including first focusing, then initial separation, and then precise separation (FISPS) and initial separation and then precise separation (ISPS) were found. The separation strategy ISPS occurred at El < 0.14 while the separation strategy FISPS occurred at El > 8.43. In addition, the transformation of the separation mechanism from ISPS to FISPS was found under different flow conditions in the fluid with the transitional rheological properties (0.21 < El < 1.10). The effect of the flow rate and the rheological property of the fluid on microparticle separation were systematically studied by the experiment. With simple structure, easy operation, high separation efficiency, the present microfluidic device would have great potentials in the biomedical and clinical applications, such as the separation of cells for different patients.