Does Saving Grace also redirect damage coming from cards with the ability of "destroy" target creature? If it does, will it only destroy the creature that has been enchanted by Saving Grace?
No, that will never work.
An effect that outright "destroys" a creature does not deal damage, so there is no damage to redirect for Saving Grace.
No. Saving Grace has no effect because destroying doesn't cause damage.[CR 701.7a]
Quite the opposite, dealing damage to a creature can result it in being destroyed.
When a creature takes damage, that damage is marked on the creature.[CR 119.3e] The next time a player would get priority, creatures with at least as much marked damage as their toughness are destroyed.[CR 704.3, 704.5g]
- Unless the source of the damage has Wither or Infect.
- Unless the creature is indestructible.
701.7a To destroy a permanent, move it from the battlefield to its owner’s graveyard.
119.3e Damage dealt to a creature by a source with neither wither nor infect causes that much damage to be marked on that creature.
704.3. Whenever a player would get priority (see rule 116, “Timing and Priority”), the game checks for any of the listed conditions for state-based actions, then performs all applicable state-based actions simultaneously as a single event. [...]
704.5g If a creature has toughness greater than 0, and the total damage marked on it is greater than or equal to its toughness, that creature has been dealt lethal damage and is destroyed. Regeneration can replace this event.