Hello experienced woodworkers

I am working on a special project (I'm actually a textile artist), and I
need to have some masonite or hardboard cut into a specific size and shape
(small squares) in some quantity.

I will have to shop this out to someone, and I need to have as ultra smooth
edges as I can get with exact size. Is what I'm looking for called laser
cutting or dye cutting, and what is the difference?

Where would I look to find someone like this to do this type of work?

Thanks for any kind help

L&D