Remove all the contents and drawers from the vanity.
Turn off/disconnect the plumbing.
Look inside for any screws that would go into the walls and remove those. Specifically around the top, base, and sides of the vanity. You might find how the sink top is attached to the base as well, splitting those will make it lighter but maybe not easier. 100% depends on the assembly.
Cut the caulk between the wall and vanity top. Probably goes all the way around and maybe under the lip.
Lift up on the corner of the top/vanity. Everything should lift up and start breaking away from the wall. It should lift with some weight but you shouldn't have to really leverage on it to move it. If it still feels attached, look for more screws.
It's probably just construction adhesive holding that part to the wall. So you can try prying that off first but sometimes they attach it with something else to the top (besides just caulk).
Thank you for the detailed response. So for that raised lip I should expect nothing but caulking on the edges holding it to the wall?
It's probably just construction adhesive holding that part to the wall. So you can try prying that off first but sometimes they attach it with something else to the top (besides just caulk).