Tyrosyl-DNA phosphodiesterase 1 (Tdp1) is a promising target for anticancer therapy due to its ability to counter the effects topoisomerase 1 (Top1) poison, such as topotecan, thus, decreasing their efficacy. Compounds containing adamantane and monoterpenoid residues connected via 1,2,4-triazole or 1,3,4-thiadiazole linkers were synthesized and tested against Tdp1. All the derivatives exhibited inhibition at low micromolar or nanomolar concentrations with the most potent inhibitors having IC50 values in the 0.35–0.57 µM range. The cytotoxicity was determined in the HeLa, HCT-116 and SW837 cancer cell lines; moderate CC50 (µM) values were seen from the mid-teens to no effect at 100 µM. Furthermore, citral derivative 20c, α-pinene-derived compounds 20f, 20g and 25c, and the citronellic acid derivative 25b were found to have a sensitizing effect in conjunction with topotecan in the HeLa cervical cancer and colon adenocarcinoma HCT-116 cell lines. The ligands are predicted to bind in the catalytic pocket of Tdp1 and have favorable physicochemical properties for further development as a potential adjunct therapy with Top1 poisons.