Kirigami-inspired cuts are an established route to stretchability in two-dimensional materials. At the nanoscale, however, cut edges are not purely geometric: they comprise discrete atomic configurations that can alter the mechanical response. In graphene, a given cut geometry fixes the edge structure; graphyne, a porous carbon allotrope with an intrinsic band gap, lifts this constraint, as identical cut geometries can yield distinct hole-edge configurations. Using molecular dynamics simulations, we report the first atomistic study of γ-graphyne kirigami (GYK), and compared with graphene kirigami. GYK reaches yield strains up to 9.6 times that of pristine γ-graphyne, with a response governed by both cut geometry and local hole-edge structure. Removing just two carbon atoms at selected edge sites further raises the yield strain by up to 35%, with little loss of yield stress. These findings identify hole-edge atomic configuration as an additional design parameter, expanding the design space for nanoscale kirigami engineering.