The development of civilizations such as ours into spacefaring, multi-planet entities requires significant raw materials to construct vehicles and habitats. Interplanetary debris, including asteroids and comets, may provide such a source of raw materials. In this article, we present the hypothesis that extraterrestrial intelligences (ETIs) engaged in asteroid mining may be detectable from Earth. Considering the detected disc of debris around Vega as a template, we explore the observational signatures of targeted asteroid mining (TAM), such as unexplained deficits in chemical species, changes in the size distribution of debris and other thermal signatures that may be detectable in the spectral energy distribution (SED) of a debris disc. We find that individual observational signatures of asteroid mining can be explained by natural phenomena, and as such they cannot provide conclusive detections of ETIs. But, it may be the case that several signatures appearing in the same system will prove harder to model without extraterrestrial involvement. Therefore, signatures of TAM are not detections of ETI in their own right, but as part of ‘piggy-back’ studies carried out in tandem with conventional debris disc research, they could provide a means of identifying unusual candidate systems for further study using other search for extra terrestrial intelligence (SETI) techniques.