The dynamic properties of the dipolar magnet CsGd(MoO4)2 have been studied. The frequency and temperature dependence of the AC susceptibility investigated in the paramagnetic region above 2 K revealed the co-existence of magnetic field induced slow and fast relaxation channels with a timescale differing by three orders of magnitude. The slow relaxation is determined by the properties of the first coordination sphere of the Gd(3+) ion and has the character of a two-phonon Orbach process. The fast relaxation is potentially attributed to a two-phonon Raman process realized via a localized phonon mode associated with the layered crystal structure. The temperature dependence of the phonon mean free path in zero magnetic field indicates significant phonon scattering below 1 K resulting from the combined effect of magnetic correlations and the scattering of dominant phonons with energies corresponding to the crystal-field levels.