Newbie: How to clamp material to cut shapes out of the center?

I finaly have my CNC machine (ShopTask 3 in 1 machine) "dialed in" and
running well.
I've done several projects on the lathe and mill and am pleased with
the outcome.

Now what I want to accomplish is to use the CNC to cut several shapes
from a single piece of flat material.

I know I can clamp the larger "base material" down and keep if from
moving, but how does one keep the cutout shape from being thrown
across the room or distorted (or both) once that last little bit of
material that holds the shape to the base material is removed.

here is an example (only a scenario):
If I had a piece of aluminium that is say 10" x 10" X .0625" thick and
wanted to cutout several dog tags in the shape of little bones, what
would be the best method of clamping to allow the parts to be cut and
not destroyed or become airborne projectiles when the cutter aproaches
that last little bit of aluminium that holds it to the big square?

Or is this an instance where you leave that last little bit and finish
the cut by hand using a dremel or such?
Thanks,
Jim