Provided it will run well under load at high speed, it is likely to be a fuel delivery problem that only applies at low speed: not a blocked filter, leaking fuel pipe, or deteriorated fuel pump. The most likely cause of failing to run slowly, but running properly at high speed and load, is obstruction of the low speed system in the carburetor. You can confirm this by adjusting the choke carefully to see if there is a choke setting that will allow it to run properly at low speed. (Of course while the choke is applied it then won't run properly at high speed: it will be far too rich.)
On the other hand if, as well as not running slowly, it will not produce full power output at high speed, the most common cause is an obstruction in the fuel system including the carburetor. The next most likely possibility is that the spark arrestor (a fine metal mesh screen across the muffler intake) is obstructed by carbon. The third most likely possibility is that the engine has lost compression.
While those are the way the probabilities run, I suggest you investigate the problem by doing the easiest tests first. If the machine is not giving full power at high speed, I recommend that you begin by testing the compression, because that is the easiest test to make. Remember, a crankcase induction 2 stroke has two compressions per revolution. If both pulses are strong, the spark arrestor is the next easiest thing to check. While the muffler is off you have the chance to inspect the side of the piston, through the exhaust port. If there are scratches up and down the piston, parallel to the cylinder bore, the piston is damaged and has to be replaced. However the bore may be damaged also: if that is the case, the machine is probably not worth fixing.
Once you have checked the compression, the spark arrestor, and the piston in that way, the next step would be to overhaul the fuel system including the carburetor.
