Lets say that I use Valorous Smite to mark a bunch of minions, and lets say they attack other members of my party except me. Because of Divine Sanction they'll take 8 damage (3 plus charisma modifier of 5). From what I recall off the top of my head minions usually die when they take damage, except damage done on attacks that miss. So, would the minions die?
Yes, because the trigger was the minion making an attack that doesn't include you. Whether or not that attack misses does not matter. The minion has to be missed by an attack that deals damage on a miss for it to ignore that damage.
Monster Manual, page 282
A minion is destroyed when it takes any amount of damage. Damage from an attack or from a source that doesn't require an attack roll (such as the paladin's divine challenge or the fighter's cleave) also destroys a minion. However, if a minion is missed by an attack that normally deals damage on a miss, it takes no damage.