The hydrophilic and hydrophobic single-walled carbon nanotube membranes were prepared and progressively applied in sorption, filtration, and pertraction experiments with the aim of eliminating three antibiotics—tetracycline, sulfamethoxazole, and trimethoprim—as a single pollutant or as a mixture. The addition of SiO2 to the single-walled carbon nanotubes allowed a transparent study of the influence of porosity on the separation processes. The mild oxidation, increasing hydrophilicity, and reactivity of the single-walled carbon nanotube membranes with the pollutants were suitable for the filtration and sorption process, while non-oxidized materials with a hydrophobic layer were more appropriate for pertraction. The total pore volume increased with an increasing amount of SiO2 (from 743 to 1218 mm3/g) in the hydrophilic membranes. The hydrophobic layer completely covered the carbon nanotubes and SiO2 nanoparticles and provided significantly different membrane surface interactions with the antibiotics. Single-walled carbon nanotubes adsorbed the initial amount of antibiotics in less than 5 h. A time of 2.3 s was sufficient for the filtration of 98.8% of sulfamethoxazole, 95.5% of trimethoprim, and 87.0% of tetracycline. The thicker membranes demonstrate a higher adsorption capacity. However, the pertraction was slower than filtration, leading to total elimination of antibiotics (e.g., 3 days for tetracycline). The diffusion coefficient of the antibiotics varies between 0.7–2.7 × 10−10, depending on the addition of SiO2 in perfect agreement with the findings of the textural analysis and scanning electron microscopy observations. Similar to filtration, tetracycline is retained by the membranes more than sulfamethoxazole and trimethoprim.