Two-dimensional monolayers are attractive for applications in metal-ion batteries because of their low ion-diffusion barrier and volume expansion. In this work, we carry out a first-principles study on electrochemical and structural properties of two-dimensional (2D) oxide monolayers and investigate their applications in metal-ion batteries. 2D transition-metal oxide monolayers (MO₂; M = Mn, Co, and Ni) with various ion-intercalation densities are systematically studied. Our calculations show that Li and Na atoms can easily be transported on the surfaces of the monolayers with low diffusion barriers because of the long binding distance. We find that Li₂MO₂ and Na₂MO₂ are stable because of negative intercalation energies and unsaturated specific energies. We show that MnO₂ has the lowest diffusion barrier, highest specific capacity, and smallest lattice expansion under Li-intercalation, but lowest cell voltage. We also find that CoO₂ shows the largest cell voltages in a wide range of ion-intercalation densities and smallest lattice expansion under Na-intercalation, and NiO₂ only gives the highest cell voltage in Li₂NiO₂ and has the largest volume expansion. We further show that Li and Na atoms in Li₂MO₂ and Na₂MO₂ move from stable-adsorption sites to metastable sites on the surfaces of oxide monolayers to reduce lattice expansion, leading to reduced cell voltages. It is expected that metal-ion batteries with particular applications and performances can be achieved in the design of these oxide monolayers.