Dediqué comes from the verb dedicar, meaning 'to dedicate' or 'to devote'. While it seems straightforward, its use in this song is quite ironic and poignant.
The title itself, "Me Dediqué A Perderte" (I Dedicated Myself To Losing You), highlights this irony. The singer 'dedicated' his efforts not to love, but to neglecting and ultimately losing his partner. This twist on a common verb makes it memorable and central to the song's theme of regret and missed opportunities.
This song is a heartbreaking confession from someone who realizes, way too late, that they single-handedly destroyed their own relationship. The singer isn't blaming anyone else; he's looking back and listing all the ways he failed his partner. He asks himself, "¿Cómo es que nunca me fijé que ya no sonreías?" (How did I never notice you weren't smiling anymore?), admitting he was so wrapped up in himself that he missed the most obvious signs of unhappiness.
The whole song is built around the devastatingly honest chorus: "Me dediqué a perderte" (I dedicated myself to losing you). He admits he was absent, closed off in his own world, and pushed his partner away. He blames his "maldito ego" (damned ego) for taking her for granted. By the time he finally tries to come back, he finds he's lost her forever and sees that she looks at him completely differently. It's a powerful story about the regret that comes from not appreciating what you have until it's gone.