All the strings of the harp cannot be damped simultaneously. The hands of the harpist are not big enough to span the whole harp. When the whole harp is sounding the harpist normally places the palms of the hands over as many strings as possible and then quickly slides or moves the left hand down and the right hand up to damp the remaining strings.
Damping all strings.
The harpist can also use the forearm of the left hand to damp the lowest octave and thus create a bigger span of strings that are damped simultaneously. This creates a more abrupt/subito effect.
Damping strings with hands and forearm.