Removing a pedestal sink is normally pretty easy unless someone has used construction adhesive or adhesive caulking to make sure it doesn’t move. Then it becomes challenging. This is one of those cases where you hope for the best, but expect the worst.
A pedestal sink sits on a base. Under the sink you will see a couple of holes that allow the installer to secure fasteners into the wall. In most cases, the sink is held to the wall at these locations and then caulked around the perimeter.
When someone has used adhesive, the sink is very difficult to remove without damaging the drywall. So expect it. You can try using a long blade to cut through the adhesive around the perimeter. What you will find is that the adhesive will be extremely hard and difficult to cut through. If you are lucky enough to be able to cut through it, cut the bottom of the sink first and then cut through the top as you support the weight of the sink.
You want to avoid having the sink pull the paper from the drywall and peel away the texture. Even if you are able to cut through the adhesive, you will have a hard bead of adhesive still stuck to the wall. You can use a sharp putty knife to remove most of it from the wall, but you will be faced with either repairing the drywall or using a larger sink to cover the damage.
In some cases, I have hit the sink to break it apart. I don’t recommend it, but as a last resort you may be faced with it. Regardless of how the sink comes off of the wall, be prepared for some drywall repair.