I have found that dish soap dries to fast sometimes. Use white lithium grease or silicone spray. remove all the air from the tube and remove the valve, squeeze the tire to break it from both sides of the rim. remove the valve stem nut.Wipe the lubricant all around the rim on the side you are going to remove it from. Then I slide the valve out of the hole and slowly remove the tube. If it wont come out wait till you get one side of the tire off the rim. Get five good size screwdrivers.
Take one of the screwdrivers and pull up one side of the tire bead over the rim. Try not to grab the tube if still in the tire. Take a second screwdriver about three/four inches from the first and pull the tire bead up over the rim. Now again about three/four inches away do the same and then with the fourth by this time the tire should be loose enough to take the one side off the rim. Very seldom, but sometimes, you need five screwdrivers.
Take a pice of wood to slide around the rim to get the rest of the tire off if you have to, but do not slide the screwdrivers. Now take out the tube, if still in and repeat the process to take the other side of the tire off same side of the rim.
Do not try to take both sides off at the same time. If you really are having a problem it could be that the wrong size tire was put on the rim. If you really want to cut it then try using wire cutters to cut the metal bead use the tin snips to cut the rubber.