Single‐atom catalysts (SACs) have received significant interest for optimizing metal atom utilization and superior catalytic performance in hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and oxygen reduction reaction (ORR). In this study, we investigate a range of single‐transition metal (STM1 = Sc1, Ti1, V1, Cr1, Mn1, Fe1, Co1, Ni1, Cu1, Zr1, Nb1, Mo1, Ru1, Rh1, Pd1, Ag1, W1, Re1, Os1, Ir1, Pt1, and Au1) atoms supported on graphyne (GY) surface for HER/OER and ORR using first‐principle calculations. Ab initio molecular dynamics (AIMD) simulations and phonon dispersion spectra reveal the dynamic and thermal stabilities of the GY surface. The exceptional stability of all supported STM1 atoms within the H1 cavity of the GY surface exists in an isolated form, facilitating the uniform distribution and proper arrangement of single atoms on GY. In particular, Sc1, Co1, Fe1, and Au1/GY demonstrate promising catalytic efficiency in the HER due to idealistic ΔGH* values via the Volmer‐Heyrovsky pathway. Notably, Sc1 and Au1/GY exhibit superior HER catalytic activity compared to other studied catalysts. Co1/GY catalyst exhibits higher selectivity and activity for the OER, with an overpotential (0.46 V) comparable to MoC2, IrO2, and RuO2. Also, Rh1 and Co1/GY SACs exhibited promising electrocatalysts for the ORR, with an overpotential of 0.36 and 0.46 V, respectively. Therefore, Co1/GY is a versatile electrocatalyst for metal‐air batteries and water‐splitting. This study further incorporates computational analysis of the kinetic potential energy barriers of Co1 and Rh1 in the OER and ORR. A strong correlation is found between the estimated kinetic activation barriers for the thermodynamic outcomes and all proton‐coupled electron transfer steps. We establish a relation for the Gibbs free energy of intermediates to understand the mechanism of SACs supported on STM1/GY and introduce a key descriptor. This study highlights GY as a favorable single‐atom support for designing highly active and cost‐effective versatile electrocatalysts for practical applications.