Hi @Korralily, thanks for contacting us!
This is correct, when you add, edit or delete files or folders, they will also sync these changes to the site and vice versa.
You can do what you're asking by signing out of the Dropbox desktop application, and then deleting the local Dropbox folder from your computer entirely. This won't affect the files on the site, so when you sign back into the desktop app, the files will simply sync down from the site into a new Dropbox folder.
If you need any further assistance, please let me know!