I have had this on several machines I have worked on and every time it has turned out to be one of the following. The air filter not on machine, cracks in the intake adapter, float not adjusted right, carb air fuel mixture not set correctly, or intake/exhaust valves not set correctly. I would start by first making sure the air filter is on the machine these ATVs will not run good without the air filter in place. The second thing I check is to make sure there is no cracks in the intake adapter and to make sure it has a good seal(this will give it to much air and cause this type problem). Next check the float level in the carb to ensure it has plenty of fuel in the bowl. I do this with carb on machine by taking a clear hose and putting on the drain tube of the bowl opening the drain with the tube running up the side the carb. If fuel level shows where the top of bowl lip meets the carb then float is set correctly if not carb will starve for fuel when you push the throttle. Another problem that can cause this is the valve setting. If the valves are to tight or to lose they will cause this type problem.
On one occasion I had a coil bad that when engine was running at high rpm it would start cutting out and miss firing. But it would rev up just would not go down the road at higher then 1/3 throttle.
From your description I do not think this is timing or ignition problem.
Curtis Underwood's post in 1992 350 Big Bear Cuts out under load was marked as the answer