Welcome to the forum. You've found the right place for help and advice.
Vibration is a relative term. What some call, severe, another might say is normal. Some are worse than others but all two stroke, single cylinder engines will vibrate to some extent. Just the nature of the beast.
Is your engine mounted solid to the frame? Adding any resilient material, rubber, tape, old innertubes etc, to the mounts will increase vibration and eventually compromise the mounting fasteners and other parts. A solidly mounted engine will not vibrate as bad as one soft mounted. There are things that can be done to make a more comfortable ride such as soft grips for your handlebars, proper chain tension and alignment and most engines will run better (smoother) after they're fully broke in.
Good luck, ride safe.
Tom