Try cleaning the carb again, could be a little crud got back in. Maybe put a new fuel line and filter in first. Steve

Fuel and impulse lines can also be problems if they are old and or cracked. Fuel filter and fuel hose are other things to check too. Since you can get some throttling out of it I would not think it is the air filter.

Carb rebuild kits are cheap. The diaphragm could be stiff.

Will check again.

I would try to richen up the high mixture alittle see if that helped? If not My guess would be the diaphram also.

The diaphragm "appeared" to be good. The high speed jet has a limiter on it, but what is strange is that it ran perfectly for the first 30 seconds after I cleaned the carb. I tried it out again yesterday and it bogged down immediately.

To make sure it is not the air filter, try running it briefly with the air filter off.

It seems that all the bases have been covered here. I`ll second the suggestion that you have a good look at the fuel line.

This sounds more like a partially blocked pickup body(fuel filter)
Remove the pickup body and try the engine once more.If it runs OK, replace the pickup body.

I took the carb apart again, removed and blew out the fuel line and filter, all is clear. Removed the limiter on the high speed needle and tried that adjustment, nothing worked. The fuel line does have some cracks in it, but I applied a little pressure to the line and it doesn't leak through. I hate to tell the guy to get a new line, but that might be the next step.

Check the four screws holding the engine pan and cylinder together.
They are located on the underside of the saw.
These screws becoming loose could cause a similar symptom.
External air gets in and causes the engine to lean out.

Good point, and will do. But why did it run perfectly for the first 30 seconds after I cleaned the carb internally and then start bogging? Subsequent restarts result in immediate bogging.

That running good for 30 seconds is why I suggested to clean the carb again, could have been some dirt in the fuel line or somewhere that clogged it up again. Haveing cleaned the carb again it might be time to try a new fuel line, it could be cracked inside the tank. I suppose you could try holding it upside down, then if the line had a crack in the tank it would suck fuel instead of air. Steve

my older mcCollough would bog down and idle fine. I cleaned the carb. Worked ok for a while, tried adjusting the fuel mixtures and it still bogged. Found cracked fuel lines were the problem.

I had exactly same problems. Blew out the carb, cleaned air cleaner, new fuel pickup, changed spark plug. Same thing, not working. Changed the fuel pickup line to carb, works like new!

I think the big mistake here is everybody is focused on the carb. Take the Pull Start cover off(where air enter to cool the cylinder) and likely you find area around the flywheel fan and spark coil packed with oily/wet saw dust. This dust can cause just enough resistance that the motor will run at low speeds but fail to accelerate(bog down). If you coax it to high speed it basically runs without spark from heat(dieseling). Clean fan,coil and cylinder fins regularly to avoid this and other problems(overheating). This post is late but may help somebody.