when an opponent Graves (Blasting through) move from its base to battlefield, and I react with star crossed to send it to its owner hand. Is Its ability that deal damge to all units still activated?

Yes — Star-Crossed blanks the damage. The trigger still goes on the chain when Graves becomes the Attacker, but it resolves doing nothing: his text deals damage equal to his Might to all enemy units here, and both of those referents point at Graves himself. Once he's back in hand he has a null Might and no location, so those instructions are Ignored (CR 359.3.f.2; FAQ #4917). No damage is marked, so nothing dies.

Two caveats. First, "when I attack" only fires if the move actually started a Combat Showdown — moving Graves onto a battlefield with no enemy units there is just a Non-Combat Showdown (Contested, no Attacker designation), so there's no trigger to react to at all. Second, Star-Crossed needs a friendly unit to pair with it, so you're bouncing one of your own units here too.