When you have projects that require your chainsaw it is disappointing to find it won't stay running. I can see why you would want to correct this issue. I was able to find a couple links that include great information for the issue your having with your chainsaw. I attached the links below. I hope this helps.
Thank you for your question on the chain saw bogging down when you throttle up the engine.
Please make sure you have a fresh fuel mix less than 30 days old.
If you have left fuel in the chain and it sat up for awhile it may have a plugged
It sounds like the engine is starving for fuel.
When this happens try pulling out the choke about half way to see if you get more power. If that works then you will need to either adjust the lower speed jet or have the carburetor cleaned or serviced.
If your carburetor has a low and high speed adjustment turn the low speed metering jet counter clockwise a 1/8 of a turn.
If your carburetor requires a special driver to adjust the carburetor you may have to take it in for the adjustment.
Please also make sure that the carburetor mounting bolts are tight so you have no air leaks.