Honda Lawnmower HRT216 TDA. Idles at normal revs then wants to shut off but doesn't?

What your describing sounds like the carburetor. It is starving for gas and as it dies the governor opens the throttle and it revs back up. It could be a jet adjustment issue or it could be debris in the carb. The carb should be removed and disembled for cleaning. It should be soaked in a good parts cleaner, blown out with compressed air and put back together with a rebuild kit. Check the fuel tank for dirt/water also. Sometimes you can clear it up with carburetor cleaner that goes into the gas tank. I would start by adjusting the jets, if that doesn't work go to the cleaner in the gas, if that doesn't work remove and clean the carb.