While mowing, my john deere 15 hp mower started running ar full throttle as if the governer was stuck. does this 15 hp engine have an external governer or is it built into the engine?

Question edited for clarity, full 'make model (what it is)'.
Question moved to Category.

It sounds like you are missing the throttle return springs that returns the throttle actuator back to closed. The draft of the engine will open the butterfly valve.

https://www.weingartz.com//assembly-diagram/john-deere-parts-lookup/model-z425-eztrak-mower-w-54inch-deck-pc9594-choke-throttle-speed-control-linkage-100000-fuel-and-air/4275-941-492791

https://www.google.com/search?q=john+deere+z425+carburetor+replacement

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fuel flow or blocked main jet
have the carby overhauled and check for full fuel flow

Make sure there isn't anything binding the deck belt or blades. Check the spindles for free movenent. If all that is good then it might be the linkage that is supposed to adjust the throttle when the engine is under load or it might be a carb issue...especially if you run ethanol gas in it.

check your fuel filter

It sounds like the choke is stuck on.

Always! ... in fact, wide open on any mower when mowing

check bearings in the spindles and check belt tensions.

Has your carburetor ever been cleaned? At least remove the bowl and clean it out of junk and see how it runs.

Two things:
1 Is fuel coming out of the fuel line. Older mowers have old fuel lines and they tend to get weak and collapse went they warm up with engine heat. Replace the old fuel line.
2 deposits in the carb. take off the air cleaner, start it up and spray a good carb cleaner in the carb until the engine dies. Put some 'seafoam' in the gas and a little in the oil and put the air cleaner back on and start the mower and mow on FULL THROTTLE. this should claen out the carb. Yes the mower will run rough for awhile.

these two cheap fixes will solve 85 % of carb problems. GOOD LUCK

main jet is clogged in carburetor. not getting any fuel.