If I understand your goal, you want to identify all tiddlers that are not system tiddlers, excluding those that have a tag that starts with $:/
Here's the filter syntax that does that:
[all[]!is[system]] -[tags[]prefix[$:/]tagging[]]
Then, you want to delete all tiddlers matching that filter.
You can do this directly using the filter tab in $:/AdvancedSearch.
Just enter the filter syntax as shown above and then press the delete button (trash can icon)
You can also do this by defining a $button that triggers $action-deletetiddler using a $filter parameter rather than a $tiddler parameter, like this:
<$button> delete content
<$action-deletetiddler $filter="[all[]!is[system]] -[tags[]prefix[$:/]tagging[]]" />
</$button>
enjoy,
-e