If you want to save the core, the method CalG mentioned of trepanning half way through from each side is feasible. In real life, one does not carelessly trepan the slug loose. You can hear a change in pitch as you get near to the cut through point, because the cut starts to sound 'tinny'.
Trepan with a groove that is a bit wider than the toolbit so you can avoid unnecessary jam ups.
When you hear the tinny sound indicating that you are almost through, hit the center with a hammer. If it moves in readily, then you're nearly far enough. You may be able to just hammer it until the thin material breaks away on one side. Or you can drive a narrow cold chisel through the thin material to help break it. Once you've got a crack right through, then typically you can break the slug out just by hammering it around and around.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)