Additive manufacturing (AM), such as directed energy deposition (DED), enables fabrication of complex geometries for critical parts at near-net shape, but creates a need for post-processing to achieve desired geometry and performance. In particular, parts made using DED are sometimes printed with a high initial surface roughness, requiring post-processing to meet application-dependent requirements. Magnetic field-assisted finishing (MAF), in which a magnetic polishing tool is manipulated by magnetic force and generates relative motion against a target surface, has been applied to smooth AM parts. An advantage of MAF is that the magnetically manipulated polishing tools can finish both external part surfaces and part interiors. In this paper, an oscillating magnetic polishing tool is proposed to smooth the inner surfaces of rectangular NASA HR-1 alloy channels made using DED. Because effective tool motion allows reduction of surface roughness and waviness, parameters that control polishing-tool motion are of great interest. This paper describes three parameters that control polishing-tool motion: number of polishing tools, magnetic field, and abrasive slurry. The effects of tool motion on the polishing characteristics are demonstrated, showing that the roughness of the interior channel surface can be reduced from several tens of micron to a sub-micron level.