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We present the AGN catalog and optical spectroscopy for the second data release of the Swift BAT AGN Spectroscopic Survey (BASS DR2). With this DR2 release we provide 1425 optical spectra, of which 1181 are released for the first time, for the 858 hard X-ray selected AGN in the Swift BAT 70-month sample. The majority of the spectra (813/1425, 57%) are newly obtained from VLT/Xshooter or Palomar/Doublespec. Many of the spectra have both higher resolution (R>2500, N~450) and/or very wide wavelength coverage (3200-10000 A, N~600) that are important for a variety of AGN and host galaxy studies. We include newly revised AGN counterparts for the full sample and review important issues for population studies, with 44 AGN redshifts determined for the first time and 780 black hole mass and accretion rate estimates. This release is spectroscopically complete for all AGN (100%, 858/858) with 99.8% having redshift measurements (857/858) and 96% completion in black hole mass estimates of unbeamed AGN (outside the Galactic plane). This AGN sample represents a unique census of the brightest hard X-ray selected AGN in the sky, spanning many orders of magnitude in Eddington ratio (Ledd=10^-5-100), black hole mass (MBH=10^5-10^10 Msun), and AGN bolometric luminosity (Lbol=10^40-10^47 ergs/s).