What exactly is "signal swing"?
"Signal swing" simply refers to the excursions of its value in time.  The units of this value can be voltage, or current, or frequency, etc., depending on the nature of the signal.  

So if you have a signal that is a sine wave with amplitude of 1, you'd say that it "swings" to 1 and -1.  If this sine wave was being clipped because of the nature of the system around it, then you'd say that the swing of the signal is being limited/clipped.