SASS How to set a Variable to equal nothing?

null or false will work (null is new in the latest version of Sass). Both will work for your example. The only advantage of null is that it disappears if you use it with a property.

@mixin myMixin($myVariable: false, $myOtherVariable: false){
  @if not $myVariable {
     //do something
  } @else {
    //do something else
  }
}

@include myMixin(false, $myOtherVariable);