I have a 2001 kawasaki 125 eliminator shuts off

If it dies when put into gear then its the side-stand switch (stand is down or switch not working)
If it dies when the clutch lever is released then either it was released too quickly with not enough revs, the engine doesnt have enough power to pull away or possibly the clutch switch is working in reverse

Good Luck
Hope this helps.
(If it does then please mark this as 'useful')
Ride Safe
Bike-Doc

I had the same problem on a 2006 125 Elimiator I bought used. As soon as 1 st gear was engaged, even with the kickstand up and before engaging the clutch , the engine died. There is a kill switch built in to the kickstand so you don't take off with the kickstand down. This switch malfunctioned. The simple fix is to wire around the kill swithch. I used a wire connector to close the circuit after cutting and stripping the wire leading to the kickstand swittch. Google " kickstand kill switch bypas"s for detail directions. It's a 10 minute fix if you have the electrical tools & fittings. Local dealer says a replacement for the switch is $50.