I had to remove a failed Exchange Server from Active Directory, the server was not going to be brought back online. This is done using the ADSI Edit tool on one of your Domain Controllers. Open ADSI Edit and right click on the ADSI Edit icon and select Connect to...
Use the drop down list to select Configuration from the Select a well known Naming Context: list. Click OK.
CN=Configuration/CN=Services/CN=Microsoft Exchange/CN=DOMAIN/CN=Administrative Groups/CN=Exchange Administrative Groups/CN=Servers
And right click on the failed server from the list of Exchange servers and select Delete. You will be prompted to confirm you want to delete the entry, click Yes.
Now if you launch the Exchange ECP and browse to Servers/Servers, hit the fresh icon and the Exchange Server will not be removed from the list.