You can hold almost anything down with painters tape and super glue. As @quicky06 mentioned using an O flute bit would be your best bet. I think if you can hold it down you would have a good chance of getting it cut.
Were you going to glue the magnetic sheet to your plywood before cutting or cutting them separately? If cutting them separately I would make the magnet slightly smaller so it would be easier to glue it on the plywood. That would give you some margin of error when gluing. What type of glue are you going to use to glue the magnetic sheet to the plywood? Since the magnetic sheet is almost like plastic I wonder what would bond it to the plywood well.
Depending on how thick, could you use a drag knife? Its magentic so you could plop it onto a flat steel plate to hold in place (maybe clamp at the edges)
I side clamped and surfaced a piece of MDF that was large enough for the whole sheet. I used double sticky tape to hold it in place.
To cut it I used a 1/8" downcut endmill with a high feed rate. It cut pretty easily, but I did small depths of cut to make sure it didn’t move on me. The material did make a mess and magnetically adhered to everything it could.
Most of those sheets are made out of PVC. I HIGHLY advise against laser cutting it. That releases hydrochloric acid and chlorine gas. The acid will degrade metals, the smoke ruins optics, and chlorine gas is so bad it has literally been used as a chemical weapon.
Idea is to glue a sheet of the magnetic material to BB side of baltic birch, probably using contact cement. Give it a couple days to cure. Then do the machining, with final steps being to cut out 2.5" disks in two stages:
1/8" downcut almost through the baltic birch, then
whatever cutter through the mag sheet layer.
I hadn’t thought about it spraying magnetic dust all over. This is sounding more and more like a bad idea.
It wasn’t horrible and just doing a few was a fun project. I also used machining to cut thru the color, but leave the black in a few areas. Not really something you can do with a drag knife. But if you’re going to make a habbit of it, a drag knife is likely way better.
I’ll have about 100 to cut. All things considered, think I’ll just make a recess on back, epoxy a magnet and move forward. I’ve liked the magnets i’ve gotten from KJMagnetics.com over the years.
At some point the USPS changed regulations on the number of magnetic lines per inch of sheet material allowed to ship through the mail. They basically cut it in half.
Because of that no one makes relatively strong magnetic sheets anymore without making the sheets really thick.
Went through this a year ago trying to find a solution to a problem for a client. Actually ended up getting some work out of it from the manufacture because no one else has ever laser cut it for them they so use drag knife/ plotter and can’t do the thicker material.