Does anyone know how one of these targets functions, what pushes it back up. Thanks for any ideas or information. Thanks

I'm not sure whether you're talking about reactive targets or pepper poppers.  PP are made of heavy armor type steel and i would guess you'd want a plasma cutter to cut them out.  The bases that i've seen are just angle iron welded together with a pin for the target to pivot down on.

Reactive targets are usually pnuematic or powerred by electric motors, sarco used to carry some surplus ones.  People make do with cardboard on furring strip frames with ropes to pop them up or on cart bases to pull them across the field of fire.

Take a look at this web page for some ideas.
http://www.mgmtargets.com/index.html