So, say I'm casting a card with convoke, and it's {3}{G}. If I tap {Elvish Mystic} for the mana, does that still reduce the cost of the card I'm casting?
No, you would either tap {Elvish Mistic} for its mana ability, or for convoke.
702.50a (http://imtgapp.com/forum/index.php?action=imtg;area=rule;number=702.50a): Convoke is a static ability that functions while the spell with convoke is on the stack. "Convoke" means "For each colored mana in this spell's total cost, you may tap an untapped creature of that color you control rather than pay that mana. For each generic mana in this spell's total cost, you may tap an untapped creature you control rather than pay that mana." The convoke ability isn't an additional or alternative cost and applies only after the total cost of the spell with convoke is determined.
Example: Heartless Summoning says, in part, "Creature spells you cast cost {2} less to cast. You control Heartless Summoning and cast Siege Wurm, a spell with convoke that costs {5}{G}{G}. The total cost to cast Siege Wurm is {3}{G}{G}. After activating mana abilities, you pay that total cost. You may tap up to two green creatures and up to three creatures of any color to pay that cost, and the remainder is paid with mana.
That's weird, because if you look at the new wording of Convoke in m15, it says "For each creature you tap while casting this spell pays for {1} or one mana of that creature's color." That makes it sound like {Elvish Mystic} would work for both, because as a mana ability you would activate it while paying its costs, while you cast it, but I'm sure you cannot.