Invitation Access Types have the option for a declination email. To create a declination email, go to Email Designs > New Email Designs > set Message Type to Confirmation. Create your email, and make sure the design name is clear this is the Declination message. After creating your declination email, go to Invitations & Confirmations > select Edit next to the appropriate Access Type > select your declination email design under Declination > Save.
If guests should not receive an email when they decline RSVP ("Not Attending" on the RSVP form), disable the declination email under Email Communications > Invitations & Confirmations > Edit > Declination email: [NONE] > Save.