Does untapping a creature save it from a spell that destroys a tapped creature?
That is correct, the target is essentially checked twice for validity, once while the spell is cast and again before it resolves. If the tapped creature is untapped before the spell has resolved then it is no longer a valid target and Murderous Compulsion will "Fizzle" (become countered), having no effect. Rule 608.2b covers this:


  608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it
  was in when it was targeted is illegal. Other changes to the game
  state may cause a target to no longer be legal; for example, its
  characteristics may have changed or an effect may have changed the
  text of the spell. If the source of an ability has left the zone it
  was in, its last known information is used during this process. The
  spell or ability is countered if all its targets, for every instance
  of the word “target,” are now illegal. If the spell or ability is not
  countered, it will resolve normally. Illegal targets, if any, won’t be
  affected by parts of a resolving spell’s effect for which they’re
  illegal. Other parts of the effect for which those targets are not
  illegal may still affect them. If the spell or ability creates any
  continuous effects that affect game rules (see rule 613.10), those
  effects don’t apply to illegal targets. If part of the effect requires
  information about an illegal target, it fails to determine any such
  information. Any part of the effect that requires that information
  won’t happen.