This will show you have to stop an alert and prevent that device from sending out all notifications.
If you only want to stop a single recipient from receiving the notifications, you may wish to instead see how to temporarily Pause notifications or remove a recipient from the alert.
To disable an alert from running you can toggle it off from the Alerts screen.
Locate the Alert you want to disable and use the toggle in the Actions column to toggle to off (gray).
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.