Purified water supply for human use, agriculture and industry is the major global priority nowadays. The advanced oxidation process based on atmospheric pressure non-thermal plasma (NTP) has been used for purification of wastewater, although the underlying mechanisms of degradation of organic pollutants are still unknown. In this study we employ two needle-type atmospheric pressure non-thermal plasma jets, i.e., indirect (ID-APPJ) and direct (D-APPJ) jets operating at Ar feed gas, for the treatment of methylene blue, methyl orange and congo red dyes, for two different times (i.e., 20 min and 30 min). Specifically, we study the decolorization/degradation of all three dyes using the above mentioned plasma sources, by means of UV-Vis spectroscopy, HPLC and a density meter. We also employ mass spectroscopy to verify whether only decolorization or also degradation takes place after treatment of the dyes by the NTP jets. Additionally, we analyze the interaction of OH radicals with all three dyes using reactive molecular dynamics simulations, based on the density functional-tight binding method. This investigation represents the first report on the degradation of these three different dyes by two types of NTP setups, analyzed by various methods, and based on both experimental and computational studies.