Is reinstalling Mavericks possible via recovery mode with two HDs and without a backup?
If you reinstall OS X from Recovery HD or the installer app (or Internet Recovery), your Mac's HD will not get erased.  If the installer needs to erase things, it will tell you, so go slowly and really read the words if you get a dialog box and choices. 

If you are concerned, install OS X onto any free USB drive and then get a good backup of the system you care not to loose.