all SQL azure tables require a clustered index: http://msdn.microsoft.com/en-us/library/windowsazure/ee336245.aspx#cir
This is by design. To answer your questions:
Removing the special index should not remove the clustered index. SQL Azure probably created the clustered index, because you didn't have one and it is a requirement in SQL Azure. I would manage clustered indexes on my own not have SQL Azure put default ones on there, just to satisfy requirements.
Update
You can only have ONE clustered index on any SQL table. There are no other clustered indexes that are managed on a table with a clustered index already existing. I hope that helps with your comment below.