How big is this thing? If your part is going to be the size of one of those big foam hand/finger things you'll have an awfully tough time making a nice part with a die and trying to shove it through the foam. At the very least you'll need a large press, and then you'll have to do a little work getting the part out of the die when you are done, risking breaking the part. Dies can be tricky if you haven't built one before.
The "ultimate" way to make your part is to find a short run shop that does abrasive waterjet cutting. No heat is introduced to the foam, its blindlingly fast, leaves a nice edge, minimal mess, etc. Rather than spend time on a die it might be to your advantage to have a 2d line drawing of your thing sent to a shop, pay a $100 setup fee, a few bucks a part and let them bang out hundred of them for you by tomorrow...
http://www.emachineshop.com/machines-kerf/water-jet-cutting.htm
If you've ever seen the Flow Corp's "Flying Bridge" on the show "American Chopper", that would be an example of waterjet cutting machine. High pressure water mixed with an abrasive slurry is shot through a sapphire tipped nozzle at an obnoxious amount of pressure. The cnc end of it is similar to laser or plasma, except it has the ability to cut plastic, wood, foam where the others can't.
-BG