First I'd like to know how you have your ignition circuit wired. We're assuming you have a Chinese 2 stroke engine. It always helps to tell us some basic information.
If you have the black to the black wire and the blue to blue and the kill switch wires, color doesn't matter spliced into the blue and black and the white wire, if you have one, is insulated away from any metal contact, then we can start there.
This problem has come up in the past and it was eventually traced to a defective magneto coil. If I recall the blue wire was the culprit and it was broken somewhere in the coil windings.
Replace the magneto coil, wire it as described above and you'll be good to go.
I'm a firm believer in having and using a kill switch. They aren't just a convenient way to shut down the engine but a safety device in the event you have a carburetor or throttle cable malfunction. They also need to be located where they are easily reached without taking your hands off the bars.
Tom