Capacitor provides low reactance to AC that means, it is alomst short for AC. Thus there is no charging.
The reactance (Xc) can be calculated as,
Xc = [1/(2 x Pi x f x C) ] Ohms
Where,
Pi = 3.14
f = AC signal frequency in Hz
C = Value of Capacitor in Farads
For DC, frequreny is 0 Hz which results in infinite reactance for any value of capacitor. Thus full applied voltage drop is created across the capacitor.
Even if you consider than capacitor charges with AC, in one half cycle, it charges with one polarity and during the other half cycle the polarity is reversed (or you can say it is discharged). Thus the net charge across the capacitor remains zero.
In clampers, the diode used, works as half wave rectifier which charges the capacitor only in one half of the input cycle which maintans a constant DC level across the capacitor and this is responsible for DC level shift at the output. In the next half cycle, the capacitor is not allowed to discharge.