How do I turn off all confirmations/reminders on a single appointment basis?

If you'd like to turn off appointment communications for a particular appointment, this can be done at the point of booking. 

When confirming the appointment details via the diary modal, clicking on Mute will allow you to stop any communications being sent for that appointment:

Note: If you book a series of recurring appointments, and choose to Mute communications, this will affect all appointments in the series.