Graphyne two-dimensional materials have been envisaged as potential useful membranes for applications such as gases separation and water desalination with very high salt rejection rates. The graphyne acetylenic linkages length defines its acetylenic holes size, thus offering a way of tuning their membrane permeability. The present study evaluates, based on density functional theory simulations, the possible use of γ-graphyne, the graphyne with the smallest acetylenic hole, to sieve Transition Metal (TM) atoms. The systematic study comprises obtaining adsorption minima for the 30 3d, 4d, and 5d TMs along with transition states for the diffusion across the γ-graphyne layer. The study reveals very small penetration barriers, below 0.5 eV, for late 3d, Pt-group, and coinage metals, whereas water molecules are found to display high penetration energy barriers above 5 eV, even when accounting for possible γ-graphyne out-of-plane deformations facilitating the water trespassing. The adsorption energy distribution of the adsorbed TMs shows that Pd and Au sieving by γ-graphyne would be specially enhanced versus their anchoring on the γ-graphyne carbon framework, thus pointing γ-graphyne as a possible effective membrane to sieve, particularly, late transition metals.