Many users make the mistake of trying to disable the alarm while inside the alarm configuration menu. The NAKO interface requires you to be on the home screen to manipulate the master audio settings.

The Nako NA-613D also features an hourly chime that beeps every hour on the hour. This is a separate function from the alarm, so even if you disable the alarm, the hourly chime may still activate. If you want to disable that as well:

Watch the top of the LCD screen for small icons: Bell Icon: The daily alarm is active. Signal/Lines Icon: The hourly chime (beep) is active.