Can I mill my opponent into defeat with Mindcrank and Duskmantle Guildmage?
Your opponent will die

The first ability from duskmantle is a delayed triggered ability:


  603.7. An effect may create a delayed triggered ability that can do something at a later time. A delayed triggered ability will contain “when,” “whenever,” or “at,” although that word won’t usually begin the ability. 
  
  603.7a Delayed triggered abilities come from spells or other abilities that create them on resolution, ...


After it is created, it does not matter what happens to the object that created it. Meaning that as soon as this ability resolves, the next time this turn that something goes to your opponents graveyard, they die.

Even though the last steps of the stack do not matter in this situation as your opponent has already lost after step 1, your stack is correct, because a spell going to the graveyard is the last part of resolving a spell and state-based actions that move your creature to the graveyard are only checked right before anyone gets priority.


  608.2k As the final part of an instant or sorcery spell’s resolution, the spell is put into its owner’s graveyard.