I had 20+ of Ikea's LOTS mirror on a wall of my retail store. After more than 8 months of having them up, one fell off and shattered to the floor. I have no idea what caused it but I knew I had to take them down because I can't have possible shards of glass landing in a customer's eye. I knew it was going to be a pain to remove them, and it was, but it really wasn't that bad. Here's the most optimal way to remove Ikea mirrors and/or double sided foam sticky tape off a wall:
1) Carefully remove the mirrors off the wall. I took a putty knife and carefully slide it behind the edges of the tape on the mirror.
2) Spray Goo Gone Spray Gel on all the areas with adhesive (I ended up using half a bottle!).
3) Get a cloth damp with a soap and warm water mixture, and "clean" the Goo Gone Gel with it. Some of the foam and adhesive will come off, but most of it won't. Don't fret!
4) Wait a couple hours. Get a paper towel or use your hand to wipe the adhesive off. It should ball up and come off fairly easily without damaging the paint (but obviously, do a small test area first).