Here I am presenting the way which I follows to remove a disconnected mailbox from the exchange 2010 server.

To get the information on mailbox of the deleted user and disconnected mailboxes you can use the following cmdlet:

Get-MailboxStatistics -Database “Mailbox Database 1” | Where-Object {$_.DisconnectDate -Notlike $NULL} | FL DisplayName, DisconnectDate, MailboxGuid

The result will be something like as give below:

DisplayName    : Username
DisconnectDate : 14-7-2011 15:01:48
MailboxGuid    : eyi9ao8d-4567-0945-489y-57yert8w7r47

Perform the following cmdlet to Remove the mailbox:

Remove-Mailbox -Database “Mailbox Database 1” -StoreMailboxIdentity def4aabd-2156-5857-858f-470efc3e6f28

After this command the mailbox will be removed