You could prevent the fall, but it is almost implausible that you will, and if you don't prevent the fall, then this approach will not mitigate the damage.
Getting pushed over a cliff is a thing. So your plan is to mitigate the fall damage by pulling someone in a straight line towards you before they fall down.
Eldritch Blast (PHB 237) is a cantrip that takes 1 action so if you would know that someone is going to fall down you could ready an action (PHB 193) to draw a friendly creature that is going over the edge towards you by casting Eldritch Blast on them.
If you correctly phrase the trigger, then it certainly works - but why you would ready your action for this or Eldritch Blast on a friendly creature, damaging them severely, instead of using a different resource is a debatable choice. That choice is further complicated by spending your action and risking interruption due to losing concentration or missing the attack roll of Eldritch Blast.
When you ready a spell, you cast it as normal but hold its energy,
which you release with your reaction when the trigger occurs. To be
readied, a spell must have a casting time of 1 action, and holding
onto the spell's magic requires concentration. If your concentration
is broken, the spell dissipates without taking effect.
Note that you would have to ready an action to do this, you can't merely cast Eldritch Blast as a reaction. For Grasp of Hadar to function as intended it also has to be your turn, so the odds for this to happen and work as you intend it are almost implausible.
Grasp of Hadar (XGtE 57):
Prerequisite: Eldritch Blast cantrip
Once on each of your turns when
you hit a creature with your Eldritch Blast, you can move that
creature in a straight line 10 feet closer to yourself.
Now we have the issue that if the creature already fell down and you don't have the action readied which means that you won't be able to cast Eldritch Blast, then it will not be possible.
Also note that if they fall down, let us say, a 600 feet cliff and you are at the bottom of the cliff and notice them falling and have enough time to ready your action during the next round because you are using the XGtE Rate for Falling (XGtE 77) and pull them towards you, then they are still falling albeit towards you and will take falling damage (PHB 183).
The rule for falling assumes that a creature immediately drops [...]
when it falls.
When you fall from a great height, you instantly descend up to 500
Effectively you will have to phrase your trigger in a way that prevents the fall from happening to mitigate the damage, and the fall has to be caused on your, and you have to perform this convoluted approach on your turn - good luck.