Lets check a couple of things first. If you slowly add choke does it smooth out and run correctly at some point. Also if the engine is on a mower if you engage the blades does it smooth out. If the answer to either question is yes, then the problem is the carb, and needs to be removed, cleaned thoroughly and have a repair kit installed.
If the answer is no then further testing will be required to rule out a governor issue. If the first test fails then try holding the throttle on the carb steady and see if it runs smooth or stumbles. Smooth would indicate a possible governor issue. Stumbles would lead back to a carb or intake leak issue.