This question cannot really be addressed without knowing whether you are using a POP or IMAP account? Since a POP account only downloads new emails from a POP3 server, if using the same computer, then I assume you have an IMAP account? With an IMAP account, where the Inbox actually resides on the server, only the messages you seek to read are downloaded, if in Mail Preferences/Accounts/Advanced you choose an option under "Keep copies of messages for offline viewing" to not keep any copies. Of course all messages remain online on the server.
More info if not applicable.
Ernie