Organic molecules can be oxidized and removed by applying, e.g. oxidants, (H2O2, Ozone), catalytic oxidation (photo-catalysts, metal catalysts), UV, etc.
In an ideal case, organics are oxidized to carbon dioxide, water and inorganic salts. e.g. CmHnO + (m+(n-1)/2)O2 -> mCO2 + n/2 H2O
Intermediate molecules may be formed during the oxidation process.