Can Serato DJ auto-mix my songs?

The short answer is no. There is no function in Serato DJ that will auto-blend two tracks together for you.

Serato DJ provides a beat matching display window that shows you markers to assist with beat matching. There is a SYNC feature that will allow your track's Beatgrids to stay in time.
 
There is also an "Autoplay" feature that will continuously play tracks one after another, however the tracks will not crossfader or mix into each other. The "Autoplay" feature is only available once Serato DJ hardware is connected. Tracks will automatically play after one another in the Offline player (no hardware connected).
 
Refer to the Serato DJ software manual for more information