Base Cost :
To exhume a corpse, you have first to remove all grave decorations, that's the gravestone and the grave fence. Then hit "E" to interact with the grave and select the "Exhume" button. You'll use up one permission for that.
After this, you have to use a shovel to dig up the corpse. You can now take it to move it elsewhere.
Finally, you can now use the grave to bury another body, or remove it at the workbench and then fill it with dirt.