The first thing you do is to cut the top of the board, where the caulking is, with a razor blade also cut the corners so when you take off the baseboard you will not take off the paint with it. Then you take a finish pry bar and hammer it all the way down to the floor where it is against the two by four on the ground. Sometimes you can start it with a wide putty knife. Then you can pull the base board back enough to get a bigger pry bar in all the way to the floor so you are pushing against the 2 by 4, this way you will not put a hole in the wall. Start from the middle of the board and work your way to the ends of the board. Doing it this way you will find it pretty easy to take the base board off without breaking it.
We take baseboards off the walls all the time. We put holes in the walls where the baseboards were to allow air into the walls to dry the walls and sometimes we inject air into the walls with tubes and an Inject-A-Dry system.
This is our flood restoration service