plane something away
to smooth off bumps or irregularities with a plane. Please plane the bumps away so that the board is perfectly smooth. Sam planed away the bumps.
plane something down
to smooth something down with a plane; to remove some material from something with a plane. I will have to plane the door down before I hang it again. I planed down the edge of the door for you.
plane something off
to remove bumps, nicks, or scrapes by planing. Plane the rough places off so the surface will be as smooth as possible. Sam planed off the bumps.