Is death from deathtouch a state based action?
Death from deathtouch is a state-based action. Specifically, this one:


  704.5h If a creature has toughness greater than 0, and it's been dealt damage by a source with deathtouch since the last time state-based
  actions were checked, that creature is destroyed. Regeneration can
  replace this event.


The triggered ability from Dissipation Field will still go on the stack, but its target will be dead by the time it resolves.