That would be the choke that you're talking about. Most pitbikes (99%) don't have a cable for the choke, you just flick the black tab to turn the choke on (butterfly closed) and once it's warm flick it back the other way to turn the choke off (butterfly open).
Yours MIGHT have a choke lever for your handle bars, I'm not familiar with your particular bike, but I don't think I've ever seen a pitbike with a choke lever on the bars.. In either case you can ride it without that cable by using the black lever on the carby.