In the present study, ab initio-based density functional theory (DFT) calculations were used to determine the effects of certain phenomena that can occur in the synthesis of Beryllium-Oxide (BeO) few-layer sheets, such as various types of defects, attaching nanocages onto the surface of graphene and attaching layers to each side of it on the mechanical and electronic properties of BeO graphene sheets. We also used the density of states (DOS) calculations to obtain a better understanding of the electronic properties of the studied nanostructures. In the first step, we calculated Young's modulus for the pristine BeO graphene sheet that was found to be equal to 1.110 TPa. Next, the effect of small and large defects on the mechanical properties of the BeO graphene-like structure was examined, and we found that extracting one Be atom resulted in a lower Young's modulus compared to that obtained after extracting one oxygen atom (1.087 TPa versus 1.104 TPa), demonstrating that Be had a greater effect on the stability and mechanical strength of BeO graphene than did oxygen. The same trend was found when comparing three atom vacancies with two missing Be atoms to those with two missing oxygen atoms. Furthermore, the effect of circular and rectangular shape defects was investigated, and the obtained results demonstrated that the increase in the diameter of defects with both shapes significantly decreased Young's modulus and band gap energy values. Additionally, due to the number of detached atoms in shape defects which are more than those of small defects, this type of defect had a more destructive effect on the structure's stability so that it decreased the Young's modulus more than small defects. Moreover, the mechanical properties of the BeO graphene nanobud structure were determined in terms of placing different numbers of Be12O12 nanocages onto the graphene surface, and a similar decreasing trend was observed for Young's modulus. Finally, we considered the mechanical properties of the bi- and three-layer BeO graphene-like structures and found that increasing the number of layers reduced Young's modulus slightly. For both of the latter phenomena of attaching nanocages and layers, the band gap energy decreased.