Double sided cutter w/ point.
Depends on required precision of work. For instance grinding down the spots , sacrificing the offending part,and a chisel is the old timer's way. Sort of like peeling off the top of a metal can. Grind what remains and you have a virgin surface. Hammer and dolly back to original.
If you're attempting to salvage the piece to work ( hammering, planing, english wheel) slow and steady. With the spot cutter, drill a centering mark for the point/ cutter so it doesn't wobble off course.
Option three for best access, side grinder off the part leaving the flanges to deal with.
I have a set of the Eastwood's that I've never used. Harbour sells cutters and you can buy four for what Eastwood wants.