  We present ALMA observations of CO $J = 2-1$ and CS $J = 5-4$ emission from
the disk around TW~Hydrae. Both molecules trace a predominantly Keplerian
velocity structure, although a slowing of the rotation velocity is detected at
the outer edge of the disk beyond ${\approx}~140$~au in CO emission. This was
attributed to the enhanced pressure support from the gas density taper near the
outer edge of the disk. Subtraction of an azimuthally symmetric background
velocity structure reveals localized deviations in the gas kinematics traced by
each of the molecules. Both CO and CS exhibit a `Doppler flip' feature,
centered nearly along the minor axis of the disk (${\rm PA} \sim 60\degr$) at a
radius of $1\farcs35$, coinciding with the large gap observed in scattered
light and mm~continuum. In addition, the CO emission, both through changes in
intensity and its kinematics, traces a tightly wound spiral, previously seen
with higher frequency CO $J = 3-2$ observations (Teague et al., 2019). Through
comparison with linear models of the spiral wakes generated by embedded
planets, we interpret these features in the context of interactions with a
Saturn-mass planet within the gap at a position angle of ${\rm PA} = 60\degr$,
consistent with the theoretical predictions of (Mentiplay et al. 2019). The
lack of a corresponding spiral in the CS emission is attributed to the strong
vertical dependence on the buoyancy spirals which are believed to only grow in
the atmospheric of the disk, rather than those traced by CS emission.
