I have cut a lot of foam with varying degrees of success. 6mm foam can be held in place using magnets, but 10mm foam is too thick for the magnets to pull onto the honeycomb and 2mm foam gets squashed by the strength of the magnets. I needed a better way to hold these sheets in place so I made my own Vacuum table.
A vacuum table is exactly as it sounds, a vacuum pump is used to pull the work piece down onto the table holding it into place for the duration of the cutting. The warped pieces of foam I'm using get pulled flat across the whole area rather than just a few points where the magnets are and the whole top surface is free of obstruction while cutting. The top layer of the bed is sacrificial, the foam doesn't need a lot of power to cut through so the mdf table doesn't mark too heavily.
A standard hoover is used to provide the vacuum for the table. A small section of foam is placed across the table and any remaining holes should be blanked over, this can be done with something as simple as sheets of paper. When the hoover is turned on the vacuum pulls the foam flat against the surface ready for cutting.
The table itself is a very simple box shape. The top layer of the table is cut with dozens of small holes through which the vacuum will be drawn. 3 braces run across the width of the table, this prevents the vacuum from deforming the box. A hoover attachment was made from multiple stacked layers of mdf, it is a tight fit on the hoover hose. The bottom end of the vacuum bed pokes out of the feed through slot. (svg here)
This vacuum table was made with a single sheet of 600x900 material. I would remake the table to fill the 600x900 cutting area of my machine. I would also make a second top layer with alignment tabs to key into place on the table, this would form a single sacrificial sheet that didn't make part of the box.
I would also run a series of smaller pipes along the front edge of the table and down to a hoover adapter to give me more flexibility over the positioning of the table and a smaller gap on the feed through slot.