Hi Mahmoud,
Based on your description, you removed the users delete right but you still wonder they can edit and save the file. Is my understanding correct?
Ideally, for saving Excel file process to work properly, users need read, write and delete rights. So this issue occurs because Excel tries to delete the temporary copy of the original workbook, but you have no permissions to delete the temporary files.
If your requirement is to let users have no permission to delete files but can edit and save them, I suggest you refer to this article:
http://serverfault.com/questions/370313/how-to-let-the-users-can-edit-in-a-shared-folder-but-not-let-them-to-delete-file
Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.
If my understanding is incorrect, please be a bit more precise explain your requirement so that I can get more accurate solutions to this problem. Im glad to help and follow up your reply.
Hope its helpful.
Regards,
George Zhao
TechNet Community Support