When you delete a record in the server table, do you do that from FM Go or from somewhere else?
What Wim asked, and...
Are the relationships similarly set for deletion in the relationship graph of the file on the server, or just in the local file on Go?
It's not symetrical because the server doesn't know where the Go file is. In other words, the mobile file could live on more than one device, so there's no realistic way for a mobile file, or really any client, to act as an external data source for a hosted file. Hence Wim and Stephen's questions about where the deletions are defined.
I am confused about your terms. By 'file' do you mean 'record'? And by 'online' do you mean 'when there is a connection between the Go file and the hosted file'?
I cannot remember a single instance where I set up cascading deletes in both directions, so I am wondering what you are trying to accomplish.