Diagnosis
This points to a fuel delivery issue. Either a clogged fuel tank vent or a dirty carburetor jet from old gas.
How to Fix It
Loosen the gas cap. If the engine then runs normally, the cap’s vent is blocked. Clean the small hole in the cap or replace it. Run it with the cap slightly loose to confirm.
If That Didn't Work
Clean the carburetor, specifically the main jet. Drain the fuel bowl (yellow screw on bottom of carb), remove the bowl and jet, and clear any debris with carb cleaner and compressed air.
Heads Up
Using gas with ethanol left sitting in the carburetor is the prime cause of this. For storage, either use a fuel stabilizer or run the engine dry using the fuel shut-off valve.