Carburetor Jet Plugged
A surging lawn mower is one of the most common problems that an engine has. It normally occurs in the springtime when you first pull out your lawn mower to get it ready for spring. You start it up and then it may slightly surge or it will be extreme. The engine gains RPM and then loses RPM and this cycle will continue nonstop until the condition is repaired.
The mechanics behind it is quite simple. The engine is being starved for fuel. The carburetor jets are plugged up and the engine will suck a little fuel to keep it running and then will start to run out of fuel. Then the engine governor comes into play. As the engine is losing RPM, the governor flyweights retract and will try to increase the RPM by opening up the throttle more. So a little fuel comes in again and the cycle repeats itself. This condition is known as a lean surge.
Air Leak
There could be another factor in play here. An air leak could have developed in the intact tract between the carburetor and the engine. When there is an air leak it will pull in more air than fuel and result in a lean mixture. The engine will run for a short time and then the surging will begin. There is less fuel to burn so it does not produce the power required to keep the engine running. The surging is usually worse at idle than at full RPM.
Elevation
I want to throw in a third possibility and that is elevation. When you live at high elevation, your carburetor fitted engines should have the main jet replaced with one for high elevation. Everyone calls it a high altitude jet, but altitude means the distance above the ground so that is not the correct term unless you are working on an airplane. This problem can also be worse at low RPM. The cause of this problem is that a standard elevation main jet has a larger hole for the fuel to flow through and you need less fuel when you are at a higher elevation because the air is less dense. Less dense air means less air molecules to burn with the fuel mixture. So you will have the wrong air to fuel ratio and will get too much fuel and run richer than normal. This condition is known as a rich surge.
By knowing the symptoms of these individual problems, this should help you diagnose them. Take your lawn mower to a reputable repair shop to resolve my lawn mower is surging.