Before deleting a custom metric it is important to know which dashboards the metric is used in. For this reason, we have improved the deletion process. After clicking 'delete' on a custom metric a warning will list the dashboards where this metric is used. If the custom metric is not in any dashboards, then you will simply see an input field to type 'DELETE' in order to delete the metric.
After confirming, the custom metric will be removed from the listed dashboards. If it is a shared dashboard it might be a good idea to check with your colleagues first as it might be important for their analysis!