Laser cutting machines are available at a number of outlets. You need to make a template that the machine will cut to produce the pieces for reassembly. These templates are 2D files and can be developed in programs such as Autodesk 123D Make. You can then generate a 2D file with your preselected card thickness and model size. This can be sent to your laser cuttting service. Ponoko is one such outlet that offers this service online.
For the lucky ones that live in a city with a techshop, can visit it and their equipment.
Additionally, a list of worldwide tech shops can be found here.
