Trying to describe how your carb works and how to fix it on a text based forum is a bit difficult.
Walbro has an excellent technical section
Service Manuals.
While you most likely have a Chineese copy on your saw down lad the manuals and have a look at the neat clean colour diagrams showing how they work.
Basically it will be either a butterfly or drum.
Note how the extra fuel gets delivered as you open the throttle.
Those holes a really really tiny and there are internal filter screens that block up as well.
What the boys have already said holds as far s carbs go. it is starving.
I like to eliminate the elecrics fist so I use a cheap in line neon tune spark tester wnich you can buy at any auto parts shop for about $ 5.
Pop it on and start the saw, if the light is still flashing as the saw is slowing down & dying then the problem is in the fuel system.
If the light goes out before the saw stops then you have an electrical problem.