Arrancar means to yank out, so your phrase means "rip out my heart" or "wrench my heart." BTW, arrancar is also used to mean "to start an engine."

Jame's explannation is right, but he hasn't replied to the question. It seems to me that in the "arráncame el corazon'', arráncame'' is not the reflexive use of arrancarse. Me means "from me", so arráncame el corazon'' means "tear out the heart from me" or tear out my heart. Am I right'

I'm pretty certain that I did reply to the question. Actually, there was no question, just statements. Please tell me which part of the implied question that I overlooked.

Your first translation (in quotes) sounds unnatural, since we don't say "the heart" in such contexts.

It means "Take my heart out" Or "rip my heart out" We use it when latin man is really in love and when a girl wants to brake up with him we tell teh girl, Take my heart out if you want to brake up with me.

Hola Tim, me llamo Cody. He visto este verbo usado en un poema se llama "La Blanca Rosa" por Jose Marti. Es mi poema favorito de la lengua espanol. El autor fue cubano y creo que te gustaria.
Arrancar significa en ingles "to rip" o "to pull'

CULTIVO UNA ROSA BLANCA... (Verso XXXIX)

Cultivo una rosa blanca,
En julio como en enero,
Para el amigo sincero
Que me da su mano franca.
Y para el cruel que me arranca
El corazón con que vivo,
Cardo ni oruga cultivo:
Cultivo la rosa blanca.

y la traducion

I have a white rose to tend
In July as in January;
I give it to the true friend
Who offers his frank hand to me.
And for the cruel one whose blows
Break the heart by which I live,
Thistle nor thorn do I give:
For him, too, I have a white rose.