After looking through the updates to Mail in Mavericks, it looks like I have bad news. There does not appear to be any way to disable Mail in Mavericks from storing local copies of messages (of course, you can save some space by preventing Mavericks from storing local copies of attachments).
If you are hard-pressed for space to the point where a few GB of local mail storage is of particular concern, then your best bet is likely either to use an email service which supports automatic message archiving (so that you can search through an archive which is stored on the server, thus freeing space on your machine that the archived messages would have taken) or routinely remove messages from your inbox and store them elsewhere (e.g., on a NAS). As it seems your goal is to have your messages readily accessible for search and other purposes, the first option is probably more likely to suit your needs.
One possible way to set up the second option (i.e., routinely moving messages out of your inbox) might work well for you. What you'll want to do is create a rule which automatically forwards your email to a second account (what email service you use for this account is entirely up to you) and then deletes the forwarded email from your inbox (you could have this done automatically once the messages is read/a certain numbers of days old or via a keyboard shortcut, whichever is preferable). This way, your local storage will remain small (only unread messages or recent messages, depending upon how you configure your rule), but the external account will have a complete archive of your messages. You can then access this archive in your browser without impacting available local free space.