In horse racing, a horse is carted away from the track because it couldn't finish the race due to injury and is unable to walk on its own.
To be physically carried from a bar or party by friends, bouncers, local authorities, and/or random people because of great intoxication and the inability to walk. Person is then placed into a vehicle and driven away.
To be taken away in a police van from a party, bar, or for general hell raising.
I had to be vanned off last night after drinking 20 shots and passing out on the hotel lobby floor.