HELPPPP - BROKEN MOPED?

Hello, i have a Baotian BT49QT-9 semi derestricted moped. To derestrict it i cut the pink throttle wire in the CDI unit, and altered the needle in the carb - i didnt alter anything to do with the exhaust - i derestricted it about 3 months ago. Recently ive been having problems with the ped. The bike will start fine when on main centre stand and will tick over nicely. However, when i push the bike off the stand it will cough and splutter and cut out. The bike is fine when going flat out down a road but is a neusance as when i come to traffic lights or junctions, as soon as i slow right down, the coughing and spluttering will kick in and will cut out. Another thing i noticed is the bike wont start when off the main centre stand - it will try to but wont and sometimes it makes a noise as if the belt is getting stuck. I dont know alot about bikes so help is appreciated :)