I'm not quite sure if I understand your situation: are you talking about trying to pull the picture off the board, or getting mono-adhesive off the back of the picture?
If you are trying to get the adhesive off the back of the picture, you might want to consider something called a rubber cement pick-up or crepe eraser. I often use one if some of my liquid adhesive seeps out from under something I have glued down (after it has dried). It is hard crepe rubber and it kind of rolls the adhesive into little bits that you can lift off with your fingers. I don't know if it will work for your situation, but it might be worth a try.
Sometimes they are hard to find. I tried Michael's, Craft Warehouse, JoAnns, Staples, Wal-Mart--and finally found it in the fine arts section of my local hobby shop. Here is a link to a picture of one.
Rubber cement pick-up