If I tried to cut all the scraps that I'm given in one session it really would take hours. Unless I'm in the mood for that I would rather do it bit by bit, so that tackling the pile doesn't become tedious.
I also use a small mat that came with a magazine. When you are cutting small pieces like this you tend to cut in the same spot over and over and the small mat saves your large cutting board. It's also easy to turn around if you're cutting multiple layers and don't want to disturb the pile. I also try to turn the scraps at different angles so I'm not always cutting parallel to the edge of the mat, again to avoid cutting over and over in the same spot.
Once everything has been reduced to neat piles of cut pieces I can file them into their containers and start ironing more scraps and storing them on the tray. It might take weeks for me to deal with the bits that Keryn gives me, but I don't get overwhelmed and sick of cutting if I do it like this.