Should I send my AP scores from highschool to a graduate school I am applying to? I scored a 3 on my Statistics test, and while it did not count for my undergraduate school as they only accept 4+, it would be a bonus when applying for a doctoral program in Clinical Psychology. However, since it was high school, would it do more harm than good?
I doubt that it would have any effect at all. You might be better to stress other, more recent things. Presumably your transcripts show proficiency in statistics sufficient for entry. 

I doubt it would do harm other than to have someone, possibly, question why you did that. And a 3 isn't a huge benefit, as your undergrad experience showed. 

However, if that is your only CV possibility pointing to knowing statistics, it would be a different matter.