When you cancel an appointment, you can mark it as a no-show as an option after you select the "Cancel" option. This will show in the client's history and also within Reports. The normal Cancellation E-mail will be sent to the client, or you can choose to not send an e-mail.
If an appointment is cancelled, it's up to you to refund your clients based on your business's refund/cancellation policy. You'll need to handle all refunds outside of Acuity in your chosen payment processor (PayPal, Stripe, Square, Braintree, or Authorize.net). Refunds cannot be issued directly inside of Acuity and will have to be manually processed in your payment processor's app!
Charging a No-Show
If it's in your policy to charge a fee or charge the full price of the appointment for a no-show, you can do this in Acuity once you have your Payment Processor set up.
If you charge a fee for no-shows, you can choose to Require a valid credit card, but don't charge for your appointments in your Payment Settings. This option will allow you to charge an amount on the client's appointment if they're a no-show. If you already require full payment at the time of booking, you can choose to give a partial refund or full refund outside of Acuity within your processor's app.
Read more about your Payment Settings in this handy guide to Accepting Payments in your Acuity Account!