In Elder Sign, does defeating a monster with a spell count as a completed task?
This is a quote from the Elder Sign rulebook, as currently posted online.  Page 8.


  Failing Rolls
  If the player is unable or unwilling to use his die results to satisfy
  any task’s requirements, the roll is considered a failed roll. He
  must discard one die of his choice from the dice pool and
  roll the remaining dice in another attempt to complete a
  task.


There is no other errata or clarifications or asides that alter this rule (other than a brief aside to confirm that yes, you can choose to intentionally fail rather than spend too many dice on one task).  It doesn't matter that you managed to complete a task on the adventure card in some other way, in your case by killing a monster with a spell.  The roll still failed.  You must still discard a die.