In this context the word "cut" is used to describe a verbal attack on the "Bitch" in question which can be a man or a woman. Usually done when the person cutting is in a bad mood and the Bitch has rubbed them up the wrong way.
"He was just being so annoying so I had to Cut a Bitch"
"Nobody better be banging on about how awesome Taylors stupid party was tonight, or I'm gonna hev to Cut a Bitch"
A female who normally would never be considered a suitable partner due to her general appearance or demeanour, but at the end of a night of unsucessful lady-hunting, suddenly becomes more appealing as a last resort at 3am.
"Did you see the ugly girl Dave went home with on saturday night?"
"Urgh yes, total 3 o'clock Princess"
"Those girls are hot, lets go over and talk to them"
"No way, that girls hot, but her friend's a 3 o'clock Princess, it's too early in the night to take that grenade.