To turn off either SMS booking confirmation/reminders or both, go to Business Setup -> Booking & Reminders -> Select Edit next to the Service category message -> remove the text in the body completely. After making your changes, click SAVE. This will no longer send an SMS.
Each service category is treated as it's own individual message. So, if you want to turn off SMS for ALL services, repeat the below steps for each service category including the Booking SMS and the Reminder SMS.