The engine needs 3 things to run. Fuel, air and spark.
Is it getting a spark when it dies? If not several causes possible Loose plug or plug wire. Seat switch, clutch switch, blade engagement switch. Ignition switch. Check connections. Maybe bad coil.
Fuel problem, check fuel solenoid (under carb) check for loose wire or remove plunger completely, venting gas cap (you checked that). Kinked fuel line. Check valve clearance.
Air, carb bolted down to engine? If loose it will suck air. You have a air filter on engine?