Publishing changed files doesn't delete anything, nor should it. You didn't say what version of EW you are using, but you can delete the files yourself - you can do that when you are in the publishing window and connected to the remote site. Select
the remote file you want to delete from the right-hand window, and click the X icon above that window.
You could experiment with the synchronize option in the publishing window, but make a back up of your local site folder before you do, in case it doesn't do what you hope it will do.