Before applying the hole saw, I drill two holes inside and tangent to the circle of material to be removed by the hole saw. This provides channels for the saw to dump the sawdust. (This may not be as important when sawing wood as it is when sawing metal.) The slug thusly has two recesses into which various forms of levers can be fit to extract the slug. [If sawing a lot of slugs, an ice tongs like tool might be worth making.]

Another approach (untried by me) would be to drive some screws partway into the back side of the slug within the cut circle so the slug has two "handles" to grab to extract it when the cut is finished.