What kind of sync options are available depends on the protocol used to talk to the servers.
If you are using IMAP or Exchange protocols (highly likely) the sync between your phone and the servers is two-way. What happens on the server gets updated on the phone and what happens on the phone gets updated on the server. If you delete something on the phone, it will be deleted on the server.
In this case, you may want to move the message to a "read it already" folder instead of deleting it.
If you downgrade to the old POP3 protocol, you can get the messages to be left on the server, but there is no two-way sync and the only folder you can download from is the "inbox". I doubt you want to go this route.
The way I do my outlook.com communications is like this:
The phone uses IMAP to sync multiple folders. I do not delete emails here, just mark them as read.
My computer uses Exchange to download the emails off the server storing them only on my computer; this results in the "old" emails "disappearing" from the phone during the next sync.
I do very little email reading from my phone.