Generally, mower engines are designed to operate at a constant speed.
Even on mowers where the operator has an engine speed control, it's not actually directly connected to the throttle disk in the carburetor. Opening and closing the throttle is the job of the governor-under light load it keeps the disk nearly closed and as load increases it opens the throttle more and more(at least up until the point where you've overloaded the engine, at which point it will start to slow down). If you have a speed control, it's adjusting the governor to a lower speed.
On a lot of push mowers, the governor is an air vane tucked up under the flywheel/fan, and often actually directly attached to the throttle disk. Typically there will be a spring on the air vane that will hold the throttle at the full open position. Air from the engine fan pushes on the air vane to close it, so in operation the air vane will settle into a spot where air speed counteracts the spring pressure. If the engine bogs and starts to slow down, the spring will pull the throttle more open, and if the engine starts to speed up the spring closes it. The operator's speed control generally will change the spring tension, although at least on the older carbs I'm familiar with there's also a gross adjustment for spring tension that lets you change the maximum operating speed and the range over which the speed control works.