Perhaps a little more explaination - having already tried many, many different ways of getting the plug out of the hole saw.

In looking at the picture, my guess is that you stuck the c-spanner into the slot on the hole saw. If so, then get a second tool to go into the slot on the opposite side, so you can work both - especially needed when you just punched through thicker material.

For a 2x cut where the plug is close to the depth of the inside of the hole saw, I have used pin punches quite successfully. I'm sure others will chime in...