The negative side effects of synthetic pesticides have drawn attention to the need for environmentally friendly agents to control arthropod pests. To identify promising candidates as botanical pesticides, we investigated the acaricidal and insecticidal activities of 44 plant-derived essential oils (EOs) against Tetranychus urticae Koch and Myzus persicae Sulzer. Among the tested EOs, Tasmannia lanceolata (Poir.) A.C.Sm. (Tasmanian pepper) essential oil (TPEO) exhibited strong acaricidal and insecticidal activity. Mortality rates of 100% and 71.4% against T. urticae and M. persicae, respectively, were observed with TPEO at a concentration of 2 mg/ml. Polygodial was determined to be the primary active component after bioassay-guided isolation of TPEO using silica gel open-column chromatography, gas chromatography, and gas chromatography–mass spectrometry. Polygodial demonstrated acaricidal activity against T. urticae with mortality rates of 100%, 100%, 61.9%, and 61.6% at concentrations of 1, 0.5, 0.25, and 0.125 mg/ml, respectively. Insecticidal activity against M. persicae was also evident, with mortality rates of 88.5%, 85.0%, 46.7%, and 43.3% at respective concentrations of 1, 0.5, 0.25, and 0.125 mg/ml. Insecticidal and acaricidal activities of TPEO were greater than those of Eungjinssag, a commercially available organic agricultural material for controlling mites and aphids in the Republic of Korea. These findings suggest that TPEO is a promising candidate for mites and aphids control.