Presently the request that is raised in support.atlassian.com cannot be deleted or hidden.
Users can only view the tickets in any status or if they have created, are a requested participant, etc

Link: https://support.atlassian.com/requests/

Suggestion:
It would be great to have a feature to be able to hide or delete the tickets at https://support.atlassian.com. keep the deleted ticket in trash. This help the customers to exclude tickets no longer required