If you installed the last SP3 for AutoCAD 2013 for Mac (AutoCAD2013SP3.dmg), than:

Here is what you can try:

- download trial version of AutoCAD 2015 for Mac - http://www.autodesk.com/products/autocad/free-trial

- install it to your Mac

- run it once (maybe this step is optional, not really sure) and close (quit AutoCAD 2015)

- try to launch AutoCAD 2013, now it should start.

- remove AutoCAD 2015 trial version from your Mac (or you can leave it - as you want).

Maxim

EDIT:

Please, report here if it helped you.