The present invention provides a chemical-mechanical polishing (CMP) composition for polishing a ruthenium-containing substrate in the presence of an oxidizing agent such as hydrogen peroxide without forming a toxic level of ruthenium tetroxide during the polishing process. The composition comprises a particulate abrasive (e.g., silica, alumina, and/or titania) suspended in an aqueous carrier containing a ruthenium-coordinating oxidized nitrogen ligand (N—O ligand), such as a nitroxide (e.g., 4-hydroxy-TEMPO). In the presence of the oxidizing agent, the N—O ligand prevents the deposition of ruthenium species having an oxidation state of IV or higher on the surface of the substrate, and concomitantly forms a soluble Ru(II) N—O coordination complex with oxidized ruthenium formed during CMP of the substrate. CMP methods for polishing ruthenium-containing surfaces with the CMP composition are also provided.