I had the same problem with my Honda Spree (85 model) 2 Stroke.
What I discovered was that the exhaust pipe (muffler) is critical to the proper operation of the engine.
If the muffler is the original or an old one, it may be restricting the exhaust flow, and not allowing the engine to rev. any faster than 20 mph. If you take it off all together, the engine probably won't run at all, (and the noise will be deafening).
Solution: What I did was drill several holes in the muffler, at the end closest to the front of the ped. This allowed some free streaming exhaust to excape which obviously had been blocked by a restricted muffler. So !!!!! Fixed. But of course the engine is now very noisey so I bought a set of ear plugs.
I'll have to bite the bullet and buy a new muffler, about US $112.00 but at least now I know what the problem was.