Presence of cyanotoxins in drinking water poses a great risk to public health. Elevated levels of cyanotoxins in drinking water can lead to acute gastroenteritis, liver diseases, and neurotoxicity. In this study, drinking water samples were collected across the eastern part of Qatar and screened using a rapid assay to detect the presence of microcystins and nodularins. The results showed that the toxin concentrations in all the water samples were below the WHO prescribed limit of 1 μg/L. Considering a worst-case scenario, toxin removal efficiencies were evaluated using ozone and ozone-hydrogen peroxide by spiking drinking water samples with microcystin-LR (MC-LR) at different oxidant dosages, toxin concentrations, water temperatures, and total organic carbon. It was found that peroxone-treated water samples have better MC-LR removal efficiency than molecular ozone at lower oxidant dosages. Nevertheless, at higher oxidant dosages, both ozonation and peroxone oxidation methods showed a similar removal efficiency. The experimental results also clearly indicated that variation in water temperature between 22 °C and 35 °C has minimal effect on the removal efficiency in both the treatment methods. It was also confirmed that the presence of organic carbon has a more profound detrimental impact than water temperature for toxin removal.