Desgarra means "tears apart" or "rips apart." It's a strong, evocative verb that conveys intense emotional pain, far beyond a simple "hurts."
In the song, the singer uses it to express the profound sorrow he feels at losing his love: "Hoy me desgarra la tristeza de perderte" (Today the sadness of losing you tears me apart). This word perfectly captures the depth of his heartbreak and makes the lyric particularly impactful.
The song opens on a man refusing news he has already been given: "Me dices que te vas y no lo acepto" [You tell me that you're leaving and I don't accept it]. He doesn't argue the point, he bargains, asking "De que vale la vida sin tu amor" [What is life worth without your love] as though the right answer might make her stay. Blame lands somewhere safely outside the two of them, on "el destino y su mala jugada" [destiny and its bad play], which made the love die in her rather than in him. The closest he comes to accounting for anything is "Contigo me forje sueños divinos" [With you I forged divine dreams], followed straight away by "Que ahora se deshacen con tu ausencia" [That now dissolve with your absence]. He made plans for two people and is left holding all of them.
The strange part is that every bit of this rides a merengue fast enough to dance to, and mid-heartbreak Crespo breaks off to call "Pequeña échate pa'aca" [Little one, come here] out at the floor. The chorus keeps conceding defeat, line after line of "Y yo no puedo retenerte" [And I can't hold you back]. Then the final line of the song quietly drops the "no": "Y yo te puedo retener" [And I can hold you back]. One missing word and he has argued himself back into thinking he can keep her, which is either the saddest thing here or the funniest, depending on how generous you feel.