Hello @HavaneseRescueInc ,
At this time, the way to do this would be to create a segment. Your criteria will be Tags > Not Tagged With > and then select and repeat for each tag you have.
Our engineers are continuing to develop the new contact dashboard, so I've attached the current feature request for "is blank" filters for tag searching / segments to your account. If and when the engineers have an update regarding this request, they'll notify you directly.