1) Using a pencil, hold your phone over the inverted coffee cup and mark where the cuts should go
2) cut through down about half an inch on both sides of the bottom of the cup, and through the base. You are making only TWO cuts -- parallel to each other across the diameter of the base of the cup
3) keep the cut portion intact to give the cup and the phone some support -- the bit you cut will collapse down a bit to hold the bottom of the phone
This is all achievable with a plastic knife, as long as it has a serrated blade.