For a large liquid argon time projection chamber (LArTPC) operating on or near the Earth's surface to detect neutrino interactions, the rejection of cosmogenic background is a critical and challenging task because of the large cosmic ray flux and the long drift time of the TPC. We introduce a superior cosmic background rejection procedure based on the Wire-Cell three-dimensional (3D) event reconstruction for LArTPCs. From an initial 1:20,000 neutrino to cosmic-ray background ratio, we demonstrate these tools on data from the MicroBooNE experiment and create a high performance generic neutrino event selection with a cosmic contamination of 14.9\% (9.7\%) for a visible energy region greater than O(200)~MeV. The neutrino interaction selection efficiency is 80.4\% and 87.6\% for inclusive $\nu_\mu$ charged-current and $\nu_e$ charged-current interactions, respectively.