How do you remove the carburetor on a Husqvarna 240e chainsaw?

With a specialty clutch tool, However you can remove most chainsaw clutches using a hammer and flat head screw driver and give it a few solid taps in counterclockwise rotation (it is reverse thread).

Is this a Chainsaw based question as I fear you have the wrong category.

Pull the chain brake handle back to release the tension off the brake band and it will come right off..

There was a number of issues with this machine and oiling, the early machine had no stregthening around the bar bols and the composit bar pad could distort crushing the oil hose ( this was sorted with the later crankcase, here you will see a squre steel block around each bar bolt ) the back of the pump housing was open on the early machine and dirt entered destroying the pump shaft gear, this was sorted with a rubber gasket at the back of the pump, let me know what you find.

Just chenk that it is mechanically sound, remove the muffler and check the condition of the piston skirt through the open exhaust port, any signs of scuffing and it will need to come apart to assess the damage.

The adjuster is a tooless system on this machine housed in the chainbrake cover, it may be the gear mechanism has jammed or stripped one of the gears, remove the brake fom the saw, remove the cross head screws covering the adjuster mechanism, clean, or replace damaged components.

It will be set at base settings, you will need to fine tune from there, the mixture screwsrequire a special tool to adjust them part no. 530035560 the screw heads have a star not a screw driver slot, max free running speed should not exceed 12500 +- 500 rpm they are not the easiest machine to tune due to the X Torque cylinder design.

Check there are no kinks in fuel line.
Make sure that the air filter isn't blocked.
Check the throttle cable is operating the throttle plate in the carburettor ok.
Ensure chain isn't too tight.
The carburettor should be a tight fit on the air inlet manifold.
It's possible that some of the jets could be blocked in the carburettor. You can try and clean these with compressed air but ensure you remove any seals gaskets, springs on the diaphragm pump , primer bulb etc as they can be damaged by the pressure.
You can also buy an aerosol can of starter fluid at your local autoparts store. This is sprayed into the carburettor to clear any partial blockages.

The 235/240E had major main bearing problems, the bearing cage on the clutch side breaks up and pinches the piston ring in, if the machines has a good spark and clean carb, i would be looking to check the it is mechanically sound, unfortunatley this means a full strip down, let me know if you need more help, i have done very many of these machines.

The symptoms indicate lean running, so check the fuel filter for plugging and the fuel lines for decay or other damage. Husky seems be having troubles with our ethanol treated fuel and may require some warranty attention. We have a year old 435 Husky that would not start after about 3 days of excellent running--warranty replaced the carburetor which seems to have us working well now. Good luck!