During the consolidation period of vacuum preloading drainage of dredged mud slurry, the clogging behaviors of the filter drainage structural layers and the core boards of prefabricated vertical drains (PVD) determine the drainage capacities of PVD. However, currently, there is a lack of comprehensive research on the evaluation criteria for these two clogging behaviors. Therefore, based on typical dredged mud slurry, typical geomembranes, and raw material core boards with different bending forms, relevant macro and micro-scale experimental studies have been carried out in this study. The research results show that (1) with the application of the gradient ratio test method, the clogging behaviors of filter membranes of PVD under graded vacuum preloading can be effectively simulated. Also, in the design of graded vacuum preloading, characteristics of equivalent pore sizes and pore structures should be emphasized to investigate the suitability of filtration and drainage performance of PVD filter membranes. (2) The compressive yield strength of core board grooves is a key factor influencing the reduction rate of flow capacity. The reduction rate of flow capacity and well resistance increment can be used as comprehensive indicators reflecting the clogging behaviors of core boards, while the bending angles and bending rates of core boards can be used as specific technical indicators. (3) The proposed clogging evaluation criteria for PVD are as follows: a filter membrane gradient ratio (GR) > 4.0, a core board bending rate >60% and a core board bending angle < 45°, or a reduction rate of flow capacity of bending drainage board > 90% or well-resistance increment > 9. Also, these criteria can be incorporated into the control indicators for drainage performance of PVD used in such types of foundations.