The engine speed is controlled by a balancing act between the governor and the governor spring. When the engine is running the governor should pull the carburetor closed, when you start the engine is there any force opposing the sparing? Trying to close the throttle?
Can you hold the governor linkage to idle and does the engine idle down? If so the governor is not working or the wrong spring is on the governor arm.
How are you adjusting the governor (or syching it to the carb)? With the control wide open, the carburetor should be wide open. Note which way the governor shaft turns to open the then throttle. Turn the shaft that direction as far as it will go, now tighten the pinch bolt Governor is now adjusted. Try to move the linkage to idle if it does not move you turned the shaft the wrong way. The linkage should move freely with no rough spots or hang ups.
NOTES. Aproperly adjusted governor should not cause surging. A lean mixture will cause surging. A carburetor cleaning may be needed.
If after properly adjusting the carb and even moving the linkage to idle does not controll the engine speed check the carbfor a loose throttle plate or a broken throttle shaft, or even the control lever loose on the shaft.
When the engine shuts off the governor naturally stops functioning and the arm will pulled to wide open by the spring, on starting the governor starts "working" and overcomes the spring closing the throttle plate to maintain set speed.