According to ikea, the main part of the mat is composed of:

“100 % polypropylene, 100 % Polyurethane, Paper, Epoxy powder coating, Steel”

Getting through that steel while simultaneously not mutilating those other layers is the challenge here. If you have to cut through it, regular bits / hole saw are not likely going to be up to the task. Rather than compromise the integrity of the mat, I’d be looking at an alternative cable management system as a simpler solution.

Not saying it’s not possible, but if you’re going through steel, that will be a real challenge.

Use a step drill bit to make the hole, then a curtain grommet.

Painter's tape, step drill bit!

Drill or punch a small pilot hole through the center of where you want the cable management hole. Then use tin snips to cut through the mat around the edges of where you want starting from the pilot hole. You can then pop in a grommet to make sure the edges aren't sharp. Just make sure to cut the right size hole for your grommet!

Make sure to get two sizes of grommet. One for the size you want, and one for the size it may end up being.

Might want to tape around where you're drilling as well (both sides!)

Step bit as others have said but first I’d put tape where you want the hole and use a razor blade to cut away the leather/leatherette first. That way you don’t mangle the cover while trying to get through the metal.

The ideal tool (depending on the size of the hole required) would be a chassis punch. Try and find an engineering shop who has them and will make the hole for you.

Does your desk already have grommet? You could pop that out and install it through both the desk and mat hole.

This! Drilling is not the answer here, cut into it with snips or make a die cut with a vise

Clamp a piece of wood on either side of it, this will prevent the outer layer from getting chewed up. Then use whatever metal-cutting drill bit you need.