Nonwoven geotextiles are commonly utilized as filter materials in drainage and filtration engineering. This study focuses on the clogging phenomenon of the nonwoven geotextile filter wrapping the blind drain in the active anti-floating technology of underground structures. In this paper, the filtration compatibility of clay-nonwoven geotextiles was evaluated using a newly developed gradient ratio test device that can apply normal stress. Two fabrication technics and four specifications of nonwoven geotextiles were used to filter clay, and the geotextiles’ clogging degree was assessed after the test. The influences of normal stresses, hydraulic gradients, and fabrication technics on nonwoven geotextile filtration performance were discussed based on results from a series of gradient ratio tests. Relevant assessment parameters (clogging coefficient, soil retention, and equivalent porosity) were also presented to quantify the clogging degree of nonwoven geotextiles after the test. Furthermore, the clogging process of nonwoven geotextiles filtering clay was initially explored, and the filtration effect of the needle-punched and heat-bonded nonwoven geotextiles was evaluated. The results showed that normal stress had a significant effect on nonwoven geotextile filtration, with needle-punched nonwoven geotextiles having better soil filtration and water permeability. Discussions on nonwoven geotextile applications in specific environments or conditions are also presented.