I don't think it would be the smartest thing in the world to cut through something containing fiberglass sheets and then install it into a system that's pushing the air you breathe around.
You could always seal it after cutting, with spray varnish or similar.
Anything you use for sealing is likely going to destroy any sound absorbing qualities that the foam might have.
Probably the best bet, IMO, is to just pull the fiberglass layer right off. It peels off very easily. Having the fiberglass layers makes it a bit easier to cut, but it will probably cut just fine without it. The foam is sufficiently firm, in my experience, to be able to install without the fiberglass layers.
FWIW, I did not find the melamine foam a superior sound absorbing product than the carpet underlay (rebond foam) that I lined most of my case with. The melamine from McMaster-Carr seems a bit fragile (fairly easy to rend) once the fiberglass was removed. I tore it accidentally with the end of the cable that runs from the CD to the sound card.
While the melamine certainly gives a cleaner look to the case than rebond foam, it did not persuade me to remove the carpet padding from my case in order to install the melamine. I might consider using it if I was starting from scratch with a new case (hmmm, I have 1.5 sheet of melamine left, maybe I need another computer.....
). Why? (1) I already own the melamine. (2) It looks a little nicer. (3) I wonder if the carpet rebond foam may deteriorate over time faster from the heat than the melamine, but I don't have any data on this either way.