Deleting attached files directly from Process View is not a feature of the product at this time. If you would like it to be, it would have to be a feature request.
Attachments are saved into documents under hidden folders. Enable viewing hidden folders in documents, browse out to the problematic documents/attachments and delete them.
Or even better, check the 'Show hidden folders' checkbox in Documents, it will stay checked and 'Open Documents' button in Documents section of Process View will let you work with documents of this particular Incident, including deletion. This setting is per-user, so documents will stay hidden for other users.