Cutting taxes also does not necessarily translate into lower tax revenues, something that was demonstrated during the 1980's.
In absolute numbers no, if you cut taxes revenues will still rise due to other factors. However, revenues will not rise as much as they would have had taxes not been cut.
If you want to test your logic, would you argue that cutting federal taxes down to say, $1.00 per person per year would lead to an increase in federal tax revenues?