Most recently, silver-metalated graphdiyne (GDY) nanomembranes have been fabricated using the wet-chemistry approach, with highly efficient response for light-driven decomposition of antibiotics (ACS Appl. Nano Mater. 2023, 6, 7395). Inspired by this exciting advance, herein for the first time we theoretically explore the key physical properties of the single-layer M-(N)GDY (M=Cu, Ag, Au) monolayers. Spin-polarized density functional theory (DFT) results reveal that metalated GDY monolayers favor a high-spin ground state, presenting a magnetic moment of 3 µB/unitcell. The sheets are characterized as small band gap magnetic semiconductors, ranging between 0.112 and 0.960 eV, in which only one spin contributes to the band gap. Ab-initio molecular dynamics results confirm the remarkable thermal stability of the constructed graphdiyne nanomembranes at 1000 K. The dynamical stability and mechanical properties at the ground state are furthermore investigated using machine learning interatomic potentials. The ultimate tensile strengths of the metalated graphdiyne lattices are found to be decent, over 6 GPa close to the ground state, but a few folds lower than the native metal-free counterparts. The presented first-principles results confirm remarkable thermal, dynamical and mechanical stability, and appealing electronic characteristics of the metalated graphdiyne nanosheets, attractive to design advanced light-weight energy storage/conversion and spintronic nanosystems.