Hi Shuan,
Kindly perform the following steps to troubleshoot the issue with Outlook 2011 for Mac.
Log into Outlook Web App and delete an email to ‘Deleted Items’. Then find where the email is when you check in Outlook client.
Could you add this account to another Outlook 2011 in different Mac? And you can check whether this problem is still existed.
You can create a new identity and set up the Office 365 account in this new identity. You can refer to this KB to create a new identity.
http://support.microsoft.com/kb/2360509
Then please refer to this article to set up Office 365 account in Outlook 2011.
http://help.outlook.com/en-us/140/gg471164.aspx
Based on your description, this is caused by the Mac, so
You can repair the identity of Outlook 2011. You can follow the steps in this KB.
support.microsoft.com/.../2360509
Thanks,
Pratik Pandya