If you part with somebody or something, it means that you are leaving the person or stopping from doing, eating or drinking something.
You can also part something if you split it in two.
In Christian Bible stories, it is told that Moses parted the waters of the Red Sea so the the Hebrews could walk across dry land between the two walls of water.
I can also say that the curtains part for the start of a play or entertainment.
However, I have never heard anyone ever say "I will part you." as a threat.