Why does your motorcycle sputter when giving it a lot of gas However shutting it off and starting it up again it runs fine. Why?

Sounds like the carburetors could be clogged or dirty. When you give it gas, it is opening up and sucking more fuel in.. so if it sputters, that means there is a clog or dirty gas. You may also want to check the air filter and if you are mechanically inclined, try taking off the carb and soak it in gas to clean the debris out. Then put them back on after a few hours.