Spectroscopic surveys of massive galaxy clusters reveal the properties of faint background galaxies, thanks to the magnification provided by strong gravitational lensing. We present a systematic analysis of integral-field-spectroscopy observations of 12 massive clusters, conducted with the Multi Unit Spectroscopic Explorer (MUSE). All data were taken under very good seeing conditions (0.6) in effective exposure times between two and 15 hrs per pointing, for a total of 125 hrs. Our observations cover a total solid angle of ~23 arcmin$^2$ in the direction of clusters, many of which were previously studied by the MACS, Frontier Fields, GLASS and CLASH programs. The achieved emission line detection limit at 5$sigma$ for a point source varies between (0.77--1.5)$times$10$^{-18}$ erg,s$^{-1}$,cm$^{-2}$ at 7000AA. We present our developed strategy to reduce these observational data, detect sources and determine their redshifts. We construct robust mass models for each cluster to further confirm our redshift measurements using strong-lensing constraints, and identify a total of 312 strongly lensed sources producing 939 multiple images. The final redshift catalogs contain more than 3300 robust redshifts, of which 40% are for cluster members and $sim$30% for lensed Lyman-$alpha$ emitters. 14% of all sources are line emitters not seen in the available HST images, even at the depth of the FFs ($sim29$ AB). We find that the magnification distribution of the lensed sources in the high-magnification regime ($mu{=}$ 2--25) follows the theoretical expectation of $N(z)proptomu^{-2}$. The quality of this dataset, number of lensed sources, and number of strong-lensing constraints enables detailed studies of the physical properties of both the lensing cluster and the background galaxies. The full data products from this work are made available to the community. [abridged]
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