Dispara comes from the verb disparar, meaning "to shoot" or "to fire". It's a strong, action-oriented word that immediately grabs attention.
In the song, the singer uses it metaphorically when he says, "Porque yo soy el que las dispara" (Because I am the one who shoots them). He's referring to the "bullets" of heartbreak, implying he's the one causing emotional pain, making it a powerful and somewhat dark confession.
Joss Favela opens by handing over a warning label instead of a love letter. "¿Alguna vez has visto esos letreros / Que dicen 'ten cuidado con el perro'?" (Have you ever seen those signs that say 'beware of the dog'?) He is the dog in that sign, and he says so before anything between them has even started, which is either unusually decent of him or the smoothest possible way to make himself interesting.
The confession then gets specific instead of vague. "Siempre me enamoran unos labios / Pero cuando pronuncian 'Te amo' / Me desaparezco como lo hace un mago" (Lips always make me fall in love, but when they say 'I love you' I vanish like a magician). My favourite bit is the line where he explains why none of it costs him anything: "Y claro que no me duelen las balas / Porque yo soy el que las dispara" (And of course the bullets don't hurt me, because I'm the one firing them). Favela sings all of this over a bright, completely unbothered arrangement, and the gap between the sunny guitars and the "aléjate de mí" (get away from me) he keeps repeating is where the song actually lives.