  Using the CLASH-VLT survey, we assembled an unprecedented sample of 1234
spectroscopically confirmed members in Abell~S1063, finding a dynamically
complex structure at z_cl=0.3457 with a velocity dispersion \sigma_v=1380 -32
+26 km s^-1. We investigate cluster environmental and dynamical effects by
analysing the projected phase-space diagram and the orbits as a function of
galaxy spectral properties. We classify cluster galaxies according to the
presence and strength of the [OII] emission line, the strength of the H$\delta$
absorption line, and colours. We investigate the relationship between the
spectral classes of galaxies and their position in the projected phase-space
diagram. We analyse separately red and blue galaxy orbits. By correlating the
observed positions and velocities with the projected phase-space constructed
from simulations, we constrain the accretion redshift of galaxies with
different spectral types. Passive galaxies are mainly located in the virialised
region, while emission-line galaxies are outside r_200, and are accreted later
into the cluster. Emission-lines and post-starbursts show an asymmetric
distribution in projected phase-space within r_200, with the first being
prominent at Delta_v/sigma <~-1.5$, and the second at Delta_v/ sigma >~ 1.5,
suggesting that backsplash galaxies lie at large positive velocities. We find
that low-mass passive galaxies are accreted in the cluster before the high-mass
ones. This suggests that we observe as passives only the low-mass galaxies
accreted early in the cluster as blue galaxies, that had the time to quench
their star formation. We also find that red galaxies move on more radial orbits
than blue galaxies. This can be explained if infalling galaxies can remain blue
moving on tangential orbits.
