The geometries stability, electronic properties, and magnetism of Y(n)O clusters up to n=14 are systematically studied with density functional theory. In the lowest-energy structures of Y(n)O clusters, the equilibrium site of the oxygen atom gradually moves from an outer site of the cluster, via a surface site, and finally, to an interior site as the number of the Y atoms increases from 2 to 14. Starting from n=12, the O atom falls into the center of the cluster with the Y atoms forming the outer frame. The results show that clusters with n=2, 4, 8, and 12 are more stable than their respective neighbors, and that the total magnetic moments of Y(n)O clusters are all quite small except Y(12)O cluster. The lowest-energy structure of Y(12)O cluster is a perfect icosahedron with a large magnetic moment 6mu(B). In addition, we find that the total magnetic moments are quenched for n=2, 6, and 8 due to the closed-shell electronic configuration. The calculated ionization potentials and electron affinities are in good agreement with the experimental results, which imply that the present theoretical treatments are satisfactory.