Delayed response sounds an awful lot like too lean a low speed mix. There could be lots of issues, perhaps the Chainsaw forum guys could give you better advice.
Things to check: if it's bogging on cutting wood: Clogged exhaust screen, chain filed too aggressively (hooked cutter teeth, rakers ground too deep). Maybe just shoving it into the wood too hard? Not likely, but you never know.
Check the fuel filter; if it looks like anything other than perfect, replace it. This especially includes any warter or grey sludge looking stuff. Even if you think you ca clean it up, replace it. Also put a new spark plug in for kicks (they're cheap).
Carb adjustment: as you open up the low speed screw, the engine idles slower (sounds odd, but it's true). Screw in (tighten) the throttle screw to make up for openig the low speed screw so it keeps idling. Don't speed up the idle to the point that the chain starts moving. With a richer low speed mix, it should accelerate more smoothly to high speed when you press the throttle.
High speed might be off too, Unless you're reall good at tuning a saw by ear, best to leave that to a pro, someone with a tach. This assumes that newer saws even have carb adjustments? Could also be a pin hole in the fuel line.
Just a couple ideas. Check the exhaust screen, spark plug, low speed carb screws first though. Good luck.
