Discutamos comes from the verb discutir, meaning "to argue" or "to discuss." In this song, Luis Miguel uses the subjunctive form "no discutamos" to express a plea or a suggestion: "let's not argue."
It's an interesting word because it immediately sets the tone for the song, which is about the aftermath of an argument and the end of a relationship. It's a common verb, but its use in this specific context, as a direct appeal to avoid conflict, makes it particularly poignant and memorable.
Luis Miguel's "No Discutamos" is a pretty blunt breakup song, and it's all about avoiding a big argument. The singer is basically saying, "Let's not fight, because after the first one, there are always more." He takes the blame, admitting, "Tuve la culpa, fue mi error / Por no decirte francamente que ya no te amo" [It was my fault, it was my mistake / For not telling you frankly that I no longer love you].
He's already asked for forgiveness, but since his ex isn't forgiving him, he's wondering what she wants him to do: "Qué quieres que yo haga / Que me quede o que me vaya" [What do you want me to do / Should I stay or should I go?]. The reason for his change of heart is pretty clear: he's found someone new. He even says, "Porque no puedes evitar / Que yo la quiera, es más lo amo" [Because you can't stop / Me from loving her, in fact, I love her]. When asked when this new love started, he's hilariously vague, claiming, "Porque por Dios por Dios / Que no, que no, que no me acuerdo" [Because by God, by God / I don't, I don't, I don't remember]. He just knows he found her, fell in love, and now he wants her, and even misses her. It's a very direct, no-frills explanation of why he's moving on.