You are trying to make a hole with a hemispherical bottom. I would remove most of the material with a regular drill, them switch to the box core bit. First, of course, try it out on a piece of scrap wood of the same type as the cutting board.
If you are just making a large diameter dimple, no need to pre-drill.
Run the drill press at its maximum speed and lower the drill slowly to minimize tear out.
AnyIn either case make sure your board is clamped in position.