Probably starving for fuel.
Check the in tank fuel filter. Also take the air filter off and look in the air box and see if you see any raw gas, especially when it's idling. Yes or NO?
Also make sure that the stud that holds the air box cover on is snug into the top of the carb. If the little stud is loose (should be good snug) on the carb the fuel pump area of the carb will be weak and suck air.
Look carefully at the carb front, on top by the mounting bolts. usually one the left side and see if you see like maybe a HL-XX (two numbers and a letter) for example HL63D or HL87D.
Since it idles ok, this indicates that the seals are ok.
I would install a new spark plug although that is doubtful yours is bad, but a bad spark plug can really make a guy feel bad after he has checked everything else.
Let us know the carb type and we can put you onto a $15 free shipping kit, carb instructions if it's a HL type, etc.
Tillotson carbs are easy to work on if its' as Tillotson.
Just be cautious and keep a heads up when re-installing the carb, if the carb to intake adapters are not aligned and seated properly at the front, a ear can break off the intake manifold as the carb bolt is tightened and that is de-pressing.
Here is what Tillotson says about such
Engine will Not Accelerate.
1. Idle adjusting screw set too lean. Enrich idle adjustment
2. Incorrect setting on diaphragm lever. Reset (PROBABLY NOT THIS BECAUSE IT RAN GOOD BEFORE)
3. Diaphragm cover plate loose. Tighten this is on the bottom of the carb, carb has to be removed.
4. Diaphragm gasket leaking. Replace
5. Main fuel orifice plugged.
#1. Lean means that the front idle mixture jet screw is in CW little bit too far, enrich means back out (CCW) about 1/4 to 1/2 turn and see if it piss revs any better. in other words if the idle mixture screw is set CW for a real good idle the setting is too lean and the saw won't rev up, set the idle mixture richer CCW little bit and test.
If you back the front idle mixture screw out little bit and the engine idles is too low, and then rev's ok you will have to go to the idle speed screw and give it little bit more.
There is a very fine sintered iron filter at the gas input to the carb, if it's restricted the saw will starve for gas, but usually it will momentarly rev then starve. This filter is finer than the in tank filter and clogs easily if the tank is nasty.