Day-camouflaged leaf-mimic katydids Typophyllum spp. have a remarkable way of evading predators as male and female forewings appear as bite-damaged leaves complete with necrotic spots. As in all other katydids, males produce sound signals to attract females by rubbing their forewings together. The biophysical properties of these special leaf-like forewings remain obscure. Here we study the wing mechanics and resonances of Typophyllum spurioculis, a new species of leaf-mimic katydid with a broad distribution in the Andes from Western Ecuador to the middle Central Cordillera in Colombia. This species performs an unusual laterally directed aposematic display, showing orange spots that simulate eyes at the leg base. At night, males are conspicuous by their loud, audible calling songs, which exhibit two spectral peaks at ca. 7 and 12 kHz. Using micro-scanning laser Doppler vibrometry we find the effective sound radiators of the wings (speculae) vibrate with three modes of vibration, two of which include the frequencies observed in the calling song. Remarkably, this resonance is preserved in the parts of the wings mimicking necrotic leaves, which are in theory not specialised for sound production. The eyespot function is discussed.