Psoriasis is an inflammatory skin disease with various symptoms of differing severities and with the reported prominent involvement of neutrophil extracellular traps (NETs). The excitation of neutrophils, e.g., by interleukin 8 (IL-8) or lipopolysaccharide (LPS), leads to the citrullination of histones and the release of protein-DNA complexes into the extracellular space, where they are digested by DNases. Our aim was to explore data on the levels of protein-complexed DNAs neutrophil elastase-DNA (NE-DNA) and myeloperoxidase-DNA (MPO-DNA), citrullinated histones (citH2, citH3, citH4), and NET-degrading enzyme DNase I in the serum of psoriatic patients with varying severities of clinical symptoms assessed with the Psoriasis Area Severity Index (PASI), Body Surface Area (BSA), and Dermatology Life Quality Index (DLQI) scores. The levels of factors were detected in 52 patients with psoriasis and 22 healthy volunteers by the enzyme-linked immunosorbent assay (ELISA). The results showed the elevated levels of NE-DNA, MPO-DNA, citH3, and DNase I in the patients with psoriasis compared to healthy volunteers (p < 0.05). Additionally, changes were noticed in the levels of NE-DNA, citH3, and DNase I, depending on the severity of symptoms (p < 0.05). In mild psoriasis (PASI < 10, BSA < 10, DLQI < 10), the suppressing activity of the enzyme caused the impaired ability to remove the physiological level of NETs, whereas in moderate to severe psoriasis (PASI ≥ 10, BSA ≥ 10, DLQI ≥ 10), the enhanced activity of DNase I failed to remove NETs due to the observed overexpression. It may, thus, be concluded that the mechanism of action of NETs, which play an undeniable role in psoriatic diseases, seem to follow two different paths depending on the severity of disease, which may be crucial in selecting potential anti-NET treatment methods.