Had a 10-10 that drove me crazy with this. It would run at first and then flood out, dribble gas out the muffer, etc. I must've had that carb apart 100 times. Turned out to be a multitude of issues. Some of it was adjustment, but it also had some gunk stuck down in the seat. After replacing the needle, triple checking the arm, and cleaning out the seat REALLY well with q-tips, it hasn't given me any issues. I think I also stretched the spring a hair to give it more seat pressure.
I have read that some people had success cleaning up a damaged seat with a mildly abrasive rubbing compound.
Also have a little homelite that did this to me. I almost dropped a match in the gas tank one day I was so mad at that saw! That turned out to be some very small bits of dirt that found their way in there, and like my 10-10 were causing the needle not to seal on the seat intermittently. Glad I didn't burn it up, it turned out to be a lot of fun and is now one of my go-to saws for smaller stuff.
Also, I assume it's the diaphragm style that hooks on to the arm? Make sure the button is hooked in there and not sitting on top of the arm. Voice of experience.
One more "also"; make sure the diaphragm gasket is on the carb body side and not on the cover side.