How to disable an alert so that it no longer runs
This will show you how to stop an alert and prevent that alert from sending out text message or email notifications.
If you only want to stop a single recipient from receiving the notifications, you may wish to instead see remove a recipient from the alert.
How to Disable an alert
Open the alerts list via Menu → Alerts and Locate the alert you want to disable.
Click the toggle switch next to the alert to disable it. The switch will move to the left (gray) to indicate it is toggled OFF. This will stop email and text message notifications for ALL recipients.

Alerts toggled off will prevent all notifications from being sent out and will remain disabled until such time as the alert is manually toggled back on (green).