Good translation. Thanks. A few corrections from a native English speaker (with explanations), verse by verse:

Por esa gran passion --> Because of the great passion
(If "por" is indicated a cause or agent, it is better translated as "because of." In this sentence, "esa" performs the role of a definite article. If there were several "great passions" around, perhaps we'd use "that" in English here, but "the" sounds more natural.)
Que dejaste encendida --> That you left burning
(Passion is not something that we usually describe as being "on." "Burning" is one translation of "encendido," and it is perfect in a metaphorical sense. We often describe a passion, romance, or love as "burning" in English.)

Y así he pasado el tiempo --> And so I have passed the time
(Keeping the same tense as the Spanish is better here, and especially the subject "I.")
Por dios que no he podido --> But by God, I can't
(More literally, "I haven't been able to," but the simple present works well.)
Me empeño en recordarte --> Your memory persists.
("Empeñarse" can mean "to make an effort" or "to try," but it also means "to persist." This would literally translate "I persist in remembering you," but this is a bit awkward.)

Te sacaré de mi alma --> I will cast you out of my heart
("Take out" is one of many ways that "sacar" can be translated, but a better translation here is "to remove" or "to expel." "Cast out" has the same meaning as "expel," and is a good way to talk about discarding something you still want... so I have taken some liberty. Of course, "alma" means "soul," but we talk more about a love being in our hearts than in our souls, so I agree with your word choice there.)
Con otro amor tan grande --> With another love as great
Tan limpio como el mío --> And as pure as mine
("Tan ... como ..." translates into a fixed expression for this type of comparison in English, "As [adjective] as [noun/pronoun]." "Clean" is not usually used to describe love, but "pure" is often used to mean something very similar.)

Espero que la vida --> I hope that life
Te de todo lo bueno --> Gives you all the best
(Not only is this more literal, it is also more poetic, in my opinion.)

Please don't think that I'm overly-criticizing your translation. It's good, but it could sound more "native."