I also had a zip lock bag too near the ice maker and it got caught up....I did the same as you, cut away as much as possible. Then I watched the subsequent ice cubes carefully and threw them out. My main concern was that it was going to harm the ice maker and since I live in an apt and the fridge belongs to landlord, I really didn't want to have to call him, nor admit what I had done.
All in all it worked out well.