Juramento means "oath", and this song is exactly that: a vow of love made with full knowledge that love hurts. It opens with a big conditional, "Si el amor hace sentir hondos dolores" (if love makes you feel deep pain) and condemns you to live "entre miserias" (in misery). Fine, says the singer: "Yo te diera mi bien por tus amores / hasta la sangre que hierve en mis arterias" (I would give you everything for your love, even the blood boiling in my arteries). That diera is an old-fashioned way of saying "I would give", the kind of grammar you hear in classic boleros.
The second half goes even darker and grander. If love is a "surtidor de místicos pesares" (a fountain of mystical sorrows) that makes a man drag "largas cadenas" (long chains), then "Yo te juro arrastrarlas por los mares / infinitos y negros de mis penas" (I swear to drag them across the endless black seas of my grief). It is melodramatic in the best way. Nobody here pretends love is easy; the whole point is choosing it anyway.