Fiber
Plasma science can seem complicated. I'll try to make it as simple and quick as possible. Plasma cutters heat the gas enough to melt it. After the metal has been heated enough to melt, it can be blown with gas to make a cut. There is much more to this process, but that's for another day. (Or, you can conduct your own research, if desired).
The laser beam generated is amplified, then fed to the cutting head via a flexible optical fibre.