A slate pool table cannot be moved in one piece. The slate bed is extremely heavy and fragile, and the table must be disassembled, moved, and then releveled and refelted. This is a job most people should hire a professional table mechanic for.
Pro tip: Hire a professional table installer for the reassembly even if you handle the teardown, since leveling and seaming the slate is skilled work.
Watch out: Slate is heavy and brittle. A dropped or flexed piece can crack, and it can crush hands and feet, so use enough people and lift it flat.