Yes. "It" is removable. I say "it" because the cup holder lining in the center console is one piece. You need to make sure you remove the center partition to remove the rubber coaster.
If it still won't budge, it could be that it's stuck due to spillage, etc. You can use a little water in there to help dissolve whatever is causing it to stick or an interior detailing product like Meguiars Quik Interior Detailer. In most acase with removable coasters, I usually just spray a little in there, let it help dissolve any residue (e.g. Coke, coffee, etc.) and then it usually just comes right out. ......use a towel to soak up excess, clean and reinsert.