Plug removal from a one piece econo hole saw used with a straight thru bore approach can be a bit rough.
With the removable mandrel in a straight through pass, just unscrew the mandrel, remove it then you can poke the plug out.
My approach is to bore the hole a tad over half way from both sides, that way you have the protruding end to grab onto to for removal. This method provides a cleaner back face.