Domar means "to tame" or "to subdue." It's a vivid verb often associated with wild animals, implying control over something powerful and untamed.
In this song, the lyrics state, "Y tú sabes que el dolor es una fiera / Y que es casi imposible de domar" (And you know that pain is a beast / And that it's almost impossible to tame). The word domar is used metaphorically to describe the difficulty of controlling or overcoming the intense pain of a broken heart, making it a memorable and impactful choice.
He is not asking her to stay. The song opens with him handing her the exit — "Tiéndeme la cama del olvido" ("Make me the bed of forgetting"), "Invéntate mil formas de querer" ("Invent a thousand ways of loving") — and then telling her to go use them: "Disfruta de las noches que tú quieras" ("Enjoy all the nights you want"). He lets the sunrise do his arguing for him. "Verás, cuando amanezca llorarás" ("You'll see, when the sun comes up you'll cry"), because what waits for her at dawn is "una fiera" that is "casi imposible de domar" ("a wild animal, almost impossible to tame").
The chorus is where the politeness drops. "Mío, mío, tu amor es mío" ("Mine, mine, your love is mine"), and "Aunque intentes remplazarme en otra piel" ("even if you try to replace me in someone else's skin"), the replacement is beaten before he starts: "Ese gran idiota está perdido" ("That big idiot is lost"). Alfredo Olivas and Carlos Rivera close on the line the whole song has been walking toward, and it is phrased as a map rather than a feeling: "Todos los caminos te harán siempre regresar" ("Every road will always bring you back").