Size segregation, which is a robust feature of sheared granular mixtures and geophysical mass flow deposits, is found to diminish in the presence of a viscous fluid. We study this inhibitive effect through coupled fluid-particle simulations of fully saturated granular flows. Granular-fluid mixture flows are modelled according to three distinct flow regimes -- free-fall, fluid-inertial, and viscous -- at different angles of inclination. Each flow regime corresponds to distinct flow dynamics and segregation behaviors. We find that segregation is indeed weaker and slower in the presence of an ambient fluid which is more so as the flow becomes more viscous. The ambient fluid affects segregation in two major ways. Firstly, buoyancy reduces the contact pressure gradients which are needed to drive large particles up, which at the same time reduces the particles' apparent weight. On the other hand, the streamwise drag force substantially changes the flow rheology, specifically the shear rate profile, thereby modifying the segregation behavior in the normal direction. Surprisingly, the fluid drag in the normal direction is negligible regardless of the fluid viscosity and does not affect segregation in a direct manner.