Metal Dies for Cloth or Leather
It sounds like you are talking about steel rule dies. 

These use a flexible or semi-flexible strip of steel sharpened along one edge. This is embedded in a backing (sometimess fibre/particle board) usually sitting in a thin profile-cut slot which supports the steel cutting edge. 

You can buy the prepared steel stock and make the dies yourself and there are also manufacturers who will make custom dies to your specification and they are relatively inexpnsive, at least by the standard of dies in general. 

They are quite well suited to cutting resonably soft materials like paper, leather, and textiles. They work best when used with some sort of press. 

I have made these myself in the past with some success when used with an arbour press. I cut the profile out of MDF with a fine coping saw and used thin shim stock to make the blades. This isn't quite as hard as the proper die stock but will just about work.