Is there any way to turn off receiving SMS on Mavericks but still get iMessages? I find it a security flaw for SMS code login for secure websites, if somebody gains access to my computer they could also login to these sites.
SMS Handoff is not a feature on Mavericks, it needs Yosemite to function
[Thanks to @tubedogg for the confirmation]
To enable it you would start from your iPhone…
Settings > Messages > Text Message Forwarding - then add your computer from the list by switching on.
That will send a code to the computer, which you then enter on your phone to confirm the function - afaik, Mavericks will never receive that number, only Yosemite.
Switching off is
Settings > Messages > Text Message Forwarding again & simply turn off forwarding that computer.