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(Abridged) We make use of the deepest VLT/MUSE observations performed so faron the Hubble Deep Field South (HDFS) to characterize the low-mass (<$10^{10}$M$_\odot$) galaxy population at intermediate redshift. We identify asample of 28 spatially-resolved emission-line galaxies in the deep (27hintegration time) MUSE data cube, spread over a redshift interval of 0.2 < z <1.4. The public HST images and multi-band photometry over the HDFS are used toconstrain the stellar mass and star formation rate (SFR) of the galaxies and toperform a morphological analysis. We derive the resolved ionized gas propertiesof these galaxies from the MUSE data and model the disk (both in 2D and withGalPaK$^{\rm 3D}$) to retrieve their intrinsic gas kinematics. We build asample of resolved emission-line galaxies of much lower stellar mass and SFR(by $\sim$1-2 orders of magnitude) than previous 3D spectroscopic surveys. Mostof the spatially-resolved MUSE-HDFS galaxies have gas kinematics consistentwith disk-like rotation, but about 20% have velocity dispersions larger thanthe rotation velocities, and 30% are part of a close pair and/or show clearsigns of recent gravitational interactions. In the high-mass regime, theMUSE-HDFS galaxies follow the Tully-Fisher relation defined from previoussurveys in a similar redshift range. This scaling relation extends also tolower masses/velocities but with a higher dispersion. The MUSE-HDFS galaxiesfollow the scaling relations defined in the local universe between the specificangular momentum and the stellar mass. However, we find thatintermediate-redshift star-forming galaxies fill a continuum transition fromthe spiral to elliptical local scaling relations, according to the dynamicalstate of the gas. This indicates that some galaxies may lose their angularmomentum and become dispersion-dominated prior to becoming passive.

Deep MUSE observations in the HDFS. Morpho-kinematics of distant star-forming galaxies down to $10^8$M$_\odot$