How about trying something called "Awesome"? I found it in the dollar store (in Michigan), can't remember which one, but it works to take out a lot of stuff. It is a yellow coloured cleaner. There were 2 different kinds, one was premixed in a spray bottle, and one was in a gallon jug that you had to mix with water. I used the full strength one. It worked to take a permanent black magic marker off of a white board. Hopefully it will work to take it off your cutting mat.