The transport properties of the thiospinel CuCrTiS4 have been investigated in detail, focusing on the possible interplay between charges and spins, and its consequence on transport, and more specifically on the thermoelectric properties. The chemical homogeneity of a CuCrTiS4 polycrystalline sample synthesized by a direct reaction of the constitutive elements has been carefully probed by X-ray diffraction and transmission electron microscopy techniques. This thiospinel exhibits below 75 K, in its paramagnetic regime, a variable range hopping (VRH) conduction, associated with a giant magnetoresistance (MR), which persists below the spin-glass transition temperature at 8 K, reaching -95% in 9 T at 5 K. All the MR data can be rescaled as a function of H/T and described using a Brillouin function with S = 3/2. This demonstrates that the paramagnetic fluctuations strongly impact the transport properties, and this is confirmed by the Seebeck coefficient which depends on the magnetic field at low temperature, with a large negative magnetothermopower (MTEP) effect of -26% at 20 K, i.e., the thermopower is reduced as the spin alignment reduces the spin entropy. This first report of MTEP in CuCrTiS4 shows that this thiospinel behaves rather similarly to strongly correlated oxides, with MR and MTEP enhanced in the case of VRH transport with paramagnetic spins, such as in cobalt misfits or colossal MR manganites.