The effective removal of dye pollutants from water and wastewater is a key environmental challenge. The present study is developed to investigate alizarin (ALI) dye and its derivations, including Alizarin blue (ABL), Alizarin purpurin (APU), Quinalizarin (AQU), Alizarin cyanin (ACY), and Alizarin Red S (ARS) removal process from water and wastewater sources, using covalent organic frameworks (COFs) nanoadsorbents. Herein, we explore the process of how dye molecules are absorbed onto COFs with precise supramolecular structures. The molecular dynamics (MD) and well-tempered metadynamics (WTMtD) simulations are used to investigate this process in aqueous solution. From the results obtained, it is clear that the intermolecular van der Waals (vdw) and π-π interactions have a significant role on accelerating the interaction between dye molecules and the COF nanostructures. This ultimately leads to the creation of a stable dye-COF complex. The dye-adsorbent average interaction energy value reaches around APU-COF1=−604.34, AQU-COF1=-515.25, ABL-COF1=−504.74, ALI-COF1=−489.48, ARS-COF1=−475.81, ACY-COF1=−273.82, AQU-COF2=−459.76, ALI-COF2=−451.46, ABL-COF2=−405.90, APU-COF2=−367.55, ACY-COF2=−287.89, ARS-COF2=−210.63 kJ/mol for dye/COF1 and dye/COF2 complexes, respectively. The primary interaction between dye and COFs is attributed to the Lennard-Jones term, resulting from the formation of a strong π-π interaction between the dye molecules and the surface of the adsorbent. Overall, our simulations confirmed that the COF1 nanostructure is more effective than the COF2 nanostructure in removing alizarin dye and its derivatives. In this study, not only the performance of two COFs in removing alizarin dye and its derivatives has been compared, but also the possibility of removing alizarin dye and its derivatives with both COFs has been examined.