We present the second data release of the MUSE Hubble Ultra-Deep Field surveys, which includes the deepest spectroscopic survey ever performed. The MUSE data, with their 3D content, amazing depth, wide spectral range, and excellent spatial and medium spectral resolution, are rich in information. Their location in the Hubble ultra-deep field area, which benefits from an exquisite collection of ancillary panchromatic information, is a major asset. This update of the first release incorporates a new 141-hour adaptive-optics-assisted MUSE eXtremely Deep Field (MXDF; 1 arcmin diameter field of view) in addition to the reprocessed 10-hour mosaic (3x3 arcmin^2^) and the single 31-hour deep field (1x1 arcmin^2^). All three data sets were processed and analyzed homogeneously using advanced data reduction and analysis methods. The 3 point-source flux limit of an unresolved emission line reaches 3.1x10^-19^ and 6.3x10^-20^erg/s/cm^26 at 10- and 141-hour depths, respectively.We have securely identified and measured the redshift of 2221 sources, an increase of 41% compared to the first release.With the exception of eight stars, the collected sample consists of 25 nearby galaxies (z<0.25), 677 [OII] emitters (z=0.25-1.5), 201 galaxies in the MUSE redshift desert range (z=1.5-2.8), and 1308 Ly{alpha} emitters (z=2.8-6.7). This represents an order of magnitude more redshifts than the collection of all spectroscopic redshifts obtained before MUSE in the Hubble ultra-deep field area (i.e., 2221 versus 292). At high redshift (z>3), the difference is even more striking, with a factor of 65 increase (1308 versus 20). We compared the measured redshifts against three published photometric redshift catalogs and find the photo-z accuracy to be lower than the constraints provided by photo-z fitting codes. Eighty percent of the galaxies in our final catalog have an HST counterpart. These galaxies are on average faint, with a median AB F775W magnitude of 25.7 and 28.7 for the [OII] and Ly{alpha} emitters, respectively. Fits of their spectral energy distribution show that these galaxies tend to be low-mass star-forming galaxies, with a median stellar mass of 6.2x10^8^M_{sun}_ and a median star-formation rate of 0.4M_{sun}/yr. We measured the completeness of our catalog with respect to HST and found that, in the deepest 141-hour area, 50% completeness is achieved for an AB magnitude of 27.6 and 28.7 (F775W) at z=0.8-1.6 and z=3.2-4.5, respectively. Twenty percent of our catalog, or 424 galaxies, have no HST counterpart. The vast majority of these new sources are high equivalent-width z>2.8 Ly{alpha} emitters that are detected by MUSE thanks to their bright and asymmetric broad Ly{alpha} line. We release advanced data products, specific software, and a web interface to select and download data sets.