Arrancar literally means "to pull out," "to tear away," or "to uproot." It's a strong verb that implies a forceful removal, much more intense than simply "to remove."
In "Olvidarte," Mike Bahía uses arrancar to express the desperate desire to forcefully remove bad memories from his mind: "De mi mente poder arrancar todos los malos recuerdos" (To be able to tear all the bad memories from my mind). This vivid imagery makes the word memorable and highlights the emotional struggle of trying to forget someone.
The song opens on an accident. "Juntos otra vez" (Together again) is a run-in, not a plan, and Mike Bahía is undone by it inside one line: "Y estás linda y se supone / Que no debería tratar de conquistarte" (And you look pretty and I'm not supposed to try to win you over). The "se supone" is doing a lot of work there. Then he gives himself away completely with "Sé que también me extrañas" (I know you miss me too), which is not a thing people say about someone they have finished with.
The chorus is where it gets funny. He announces "Te borré de mi memoria" (I erased you from my memory) while recalling her in detail, and what he wants out of his head is "Todos los malos recuerdos" (All the bad memories), filed one verse after he called her "la preferida" (the favorite). By the bridge he is writing rules, and they read like rules for himself rather than for her: "No me llames, no me escribas" (Don't call me, don't write to me). The last half-minute is that same line about the bad memories, over and over, fading out. Somebody who had actually forgotten would not need the reminder that many times.