In this work, we investigate the magnetic damping and spin pumping response of YIG-based bilayers incorporating vanadium (V) as the normal metal layer via broadband ferromagnetic resonance (FMR) measurements as a function of YIG thickness. We show that the apparent enhancement of the Gilbert damping in YIG/V bilayers cannot be solely attributed to spin pumping. Instead, two-magnon scattering (TMS) plays a dominant role in governing the thickness dependence of the damping in the nanometer regime. By applying a thickness-dependent damping model that accounts for both spin pumping and two-magnon scattering contributions, we successfully disentangle the different relaxation contributions. Our analysis reveals that neglecting two-magnon scattering leads to an overestimation of the spin-pumping contribution and consequently to unphysically large values of the effective spin-mixing conductance. After isolating the intrinsic spin pumping contribution, we extract a thickness-independent effective spin-mixing conductance of $g^{\uparrow\downarrow}_{\mathrm{eff}} = 1.33 \times 10^{18}~\mathrm{m^{-2}}$. These findings provide a more accurate framework for quantifying spin transport parameters in FM/HM systems and emphasize the necessity of accounting for extrinsic damping mechanisms when interpreting spin pumping and inverse spin Hall effect experiments.