I'm not sure (ie, may be proven incorrect) that you can delete messages using this API. The MSDN article for Microsoft.Exchange.Data.Transport.Email Namespace says this:
The Microsoft.Exchange.Data.Transport.Email namespace contains types that support creating, reading, writing, and modifying e-mail message.
And further inspection of the members available on the EmailMessage
class suggest you can access various properties, but there's no "delete" operation/method available.
Depending on your scenario, you might have better luck using a tool like Outlook Redemption which will allow low-level programmatic access to Outlook and/or Exchange (but may not be appropriate if you need to go via exchange web services).