Syntax for if/else condition in SCSS mixin

You could try this:

$width:auto;
@mixin clearfix($width) {

   @if $width == 'auto' {

    // if width is not passed, or empty do this

   } @else {
        display: inline-block;
        width: $width;
   }
}

I'm not sure of your intended result, but setting a default value should return false.

You can assign default parameter values inline when you first create the mixin:

@mixin clearfix($width: 'auto') {

  @if $width == 'auto' {

    // if width is not passed, or empty do this

  } @else {

    display: inline-block;
    width: $width;

  }
}

You could default the parameter to null or false.
This way, it would be shorter to test if a value has been passed as parameter.

@mixin clearfix($width: null) {

  @if not ($width) {

    // if width is not passed, or empty do this

  } @else {

    display: inline-block;
    width: $width;

  }
}