Why does the emitter follower clip?
The emitter follower can only pull the output voltage up (positive), it can't push the output down.

Rload and Re form a voltage divider between Ground and -12V.  If the transistor wasn't there, the output voltage produced by the Re/Rload divider would be about -2.1 volts, and that is what your graph shows.  When the base voltage goes below about -1.5 volts, the transitor will be cut off, and will have no effect on the output voltage.