I don't think there's a button or function to "clear" or erase a single saved registration.
On my Yamaha keyboards an "empty" or unsaved registration normally contains whatever parameter values the keyboard uses for its default settings. So one option might be to press and hold the PIANO ROOM button to reset the DGX-660 to its default settings as described on page 27 of the Owner's Manual, then save those default settings to the registration that you want to "clear."
However, I know that my Yamaha keybords also have a flag at the beginning of each registration to indicate whether that registration has been saved. I don't remember if I tried experimenting with that flag, but it might be that saving the default settings to a particular registration will not accomplish what you want-- i.e., when you recall the registration it will reset the keyboard to its default piano sound, rather than having no effect or leaving all of the current settings (whatever they may happen to be) untouched, such as if you accidentally hit one of the registration buttons and inadvertently change everything.
If you absolutely must clear the registrations, the only way I know of-- without trying to use a computer to "hack" the registration memories-- is to clear the keyboard's backup memory as described on page 52 of the Owner's Manual. Naturally, that will also erase any registrations you might want to keep, as well as all other settings in the keyboard's backup data. Thus, you would need to write down a complete and accurate listing of all the registration settings and other backup data you want to keep, then clear the keyboard's backup data, then reenter and resave the specific registrations and other settings that you hadn't wanted to erase. That's obviously a lot of work, and is subject to errors and oversights.