1. to dump someone; to leave behind
2. to put someone to work <for you> (originally like a pimp to put his ho on the street to work for him as a prostitute).
Colloquially is often used with the verb "kick" as to "kick <somebody> to the curb".
2. She don't clean house AND makes you pay for everything!? You need to kick that skank to the curb and tell her to earn her keep.