Grayson's background is initially unrelated in the plot of The Dark Knight Strikes Again. However, the later work All Star Batman & Robin the Boy Wonder, which is said to be the canonical start of Miller's Batman works following Batman: Year One, showed Grayson with a tragic background. During the events of All Star, Robin is shown as part of The Flying Graysons performing as Bruce Wayne watches in the audience. His parents are shot and killed by a thug Batman tracks and beats. Just to make things worse for the child, Grayson is abducted by Batman who says that he'll be his new ward and that he's "drafted into this war".
Batman's training of the boy consists of physical abuse as well as keeping him entrapped in the Batcave while forcing him to forage for his own food (which leads to a brief confrontation when Batman threatens Alfred for giving the boy food). Over time, Grayson becomes obsessed with finding his parents' killer and starts to become all the more aggressive as Robin. In one of the comic's most notorious incidents, Batman and Robin lure in Green Lantern and provoke him into a fight in a completely yellow room when Robin steals his ring. Robin comes close to murdering Green Lantern before he is oddly stopped by Batman.
With this background in mind, it sets up an understanding of Grayson's role in The Dark Knight Strikes Again where he is a villain. Thus, he is the tragic consequence of Miller's Batman.
The Dark Knight Strikes Again
In his first appearance, Grayson murders the superhero The Guardian, taunting the dying hero (whom Grayson has stabbed in the back) when The Guardian refuses to believe he is the Joker, stating the villain's death in The Dark Knight Returns. Nevertheless, Grayson, referred as the "New Joker" goes on to murder The Creeper, showing his relentlessness. During a later fight against The Question and The Martian Manhunter, Grayson murders the latter, adding another superhero to his kill count.During an encounter with Saturn Girl, Carrie (who became Robin in The Dark Knight Returns and is now Catgirl) is warned that she will be attacked by a new Joker. Carrie dismisses this vision as she previously fought and seemingly killed the new Joker not that long ago. However, Grayson appears towards the end of the narrative, having captured and tormented Carrie but is stopped by Batman from killing her. Grayson reveals himself, showing himself in his old Robin garb, and states he was in love with Batman. Batman taunts Grayson with insults about how he fired Grayson for being a weakling that "couldn't cut the mustard". It is heavily implied that Grayson was fired for his incompetence in the field.
Grayson states that he underwent radical gene therapy and can regenerate as long as there is something of him left. He demonstrates this when he catches his own head after Batman decapitates him. Batman accesses a opening to a lava pit beneath the Batcave with the intent of trapping Grayson in the lava so it would eradicate every last trace of him. Grayson manages to escape this fate for a time and duels Batman until Batman throws himself and Grayson into the lava pit. Superman saves Batman from death while Grayson falls to his destruction.