Its time for a diaphragm (rebuild) kit in that carburetor.
If you haven't already done so, replace the weighted fuel filter inside the tank. It has a felt element inside of it which will pack up with debris over time. You can't clean it; it must be replaced.
You said you already installed new fuel line. Good.
Now about the carburetor...That saw should use a Walbro HD series carbuetor. It works much like the carbs found in some snowmobiles and almost all jetskis, just on a much smaller scale. Those little saw carburetors use fuel pump diaphragms which eventually grow hard and brittle with exposure to gasoline. It is probably time for you to install a kit in that carburetor.
Take the carb off the saw, disassemble it, and go get a rebuild kit. Your carb should take a part number K10-HD kit. You can find one online or at your local small engine shop. After giving the carburetor a good cleaning, check the fuel strainer screen on the fuel pump side of the carburetor, and be SURE it is clean. They are known to become blocked with sawdust.
Also, check the gasket which goes between the carburetor and the intake manifold. It must be in good shape or you'll have an air leak.
Once you get ahold of a kit, reassemble the carburetor with fresh diaphragms and gaskets, set the hi and lo speed adjusters out 2 turns each, and crank it up. The engine should run fairly well with those settings. Once you warm the saw up, adjust the low speed adjuster until the saw idles smoothly and accelerates cleanly. You want the low speed side to be set lean enough that the engine doesn't flood out, but rich enough that it will accelerate cleanly when you get on the throttle.
Once the low-speed circuit has been adjusted, hold the throttle wide-open and turn the high speed screw in until the engine screams and begins to bog out. Then back it off until the engine begins to stumble (burble) slightly. Leave it there. You want a chainsaw to run rich at WOT when the engine is not under a load, because when you put a load on it, the engine will need more fuel.
Any questions, just ask! I fix lawn equipment and saws for a living and have lots of experience.