I vs I’ve

The first is in the simple past tense ("mentioned" is a past tense verb); the second is in the present perfect tense ("mentioned" is a past participle).

Though the two tenses have different uses, their uses sometimes overlap. This is one of those situations where both can be used - talking about an event in the recent past.

So they are both correct.

I could be wrong but I'm guessing that your confusion comes from the contraction of "I have" to "I've" which makes that verb phrase look kind of like a pronoun in writing. Think: "as I have mentioned" instead of "as I've mentioned." As for their usage, I remember from when I studied French and we learned the imperfect and perfect tenses, we were taught that there's no black and white about when to use which. In this case we're dealing with the simple past and the perfect, but I think that it's the same kind of situation: the differences between the two are slight and nuanced and there's no rule book about when to use which.

Ben's got it right. 'As I mentioned before' refers to some specific time, likely one the listener can recall from the recent past (probably during the speaker's speech). 'As I've mentioned before' likely refers to something that may have been said quite some time in the past. Just a rule of thumb.