That is definitely not a real tree, but the concept is fun. If you want yours flat similar to that you'll have to be very careful about what branches you trim off to do it.
You could try boiling your tree in water to soften the wood, then wiring it flat, or gently pressing it between two boards or something, and let it dry like that. A heavy coat of hard drying acrylic might help hold everything in place.
This is all me brainstorming, though. I've certainly never tried it, and haven't run into anything similar.