[Abridged] Asteroid mining is not necessarily a distant prospect. Hayabusa2 and OSIRIS-REx have recently rendezvoused with near-Earth asteroids and will return samples to Earth. While there is significant science motivation for these missions, there are also resource interests. Space agencies and commercial entities are particularly interested in ices and water-bearing minerals that could be used to produce rocket fuel in space. The internationally coordinated roadmaps of major space agencies depend on utilizing the natural resources of such celestial bodies. Several companies have already created plans for intercepting and extracting water and minerals from near-Earth objects, as even a small asteroid could have high economic worth. However, the low surface gravity of asteroids could make the release of mining waste and the subsequent formation of debris streams a consequence of asteroid mining. Strategies to contain material during extraction could still eventually require the purposeful jettison of waste to avoid managing unwanted mass. Using simulations, we explore the formation of mining debris streams by integrating particles released from four select asteroids. Radiation effects are included, and a range of debris sizes are explored. The simulation results are used to investigate the timescales for debris stream formation, the sizes of the streams, and the meteoroid fluxes compared with sporadic meteoroids. We find that for prodigious mining activities resulting in the loss of a few percent of the asteroid's mass or more, it is possible to produce streams that exceed the sporadic flux during stream crossing for some meteoroid sizes. The result of these simulations are intended to highlight potential unintended consequences that could result from NewSpace activity, which could help to inform efforts to develop international space resource guidelines.