I’ve never heard the ‘expression’ “monkey it up” until today.
I suspect it was a racist word substitution for “fuck it up” or “muck it up”. Yeah, he probably meant to say “muck it up’, but because of the ‘m’ and the ‘k’ sounds he made a Freudian slip revealing what he thinks about a black rival for office.

I have heard the expression “monkeying around” but always just referring to kids playing unheedfully with Dad’s expensive equipment or tossing projectiles in front of the glass cabinet with valuable stuff in it. I am sure there are those who have used it to single out minority kids playing though…..