Metallodrugs provide important first-line treatment against various forms of human cancer. To overcome chemotherapeutic resistance and widen treatment possibilities, new agents with improved or alternative modes of action are highly sought after. Here, we present a click chemistry strategy for developing DNA damaging metallodrugs. The approach involves the development of a series of polyamine ligands where three primary, secondary or tertiary alkyne-amines were selected and ‘clicked’ using the copper-catalysed azide-alkyne cycloaddition reaction to a 1,3,5-azide mesitylene core to produce a family of compounds we call the ‘Tri-Click’ (TC) series. From the isolated library, one dominant ligand (TC1) emerged as a high-affinity copper(II) binding agent with potent DNA recognition and damaging properties. Using a range of in vitro biophysical and molecular techniques—including free radical scavengers, spin trapping antioxidants and base excision repair (BER) enzymes—the oxidative DNA damaging mechanism of copper-bound TC1 was elucidated. This activity was then compared to intracellular results obtained from peripheral blood mononuclear cells exposed to Cu(II)–TC1 where use of BER enzymes and fluorescently modified dNTPs enabled the characterisation and quantification of genomic DNA lesions produced by the complex. The approach can serve as a new avenue for the design of DNA damaging agents with unique activity profiles.