And use a backing board (an old scrap of foam core) so the tip of the blade, dulled by passing over whatever hard surface you use, is not actually cutting the board itself.

I just cut 20 40x32 boards down to 16x20, 20x24, and 24x28 using my new Logan 750 SimplexPlus. Took about 30 minutes. If you are going to cut much, get one of these! They are only $230 or so (I got mine from http://allartsupplies.com ) and it has brought joy into cutting mats. Merry Christmas! Merry Christmas, Everyone!