Sounds to me like the engine does not like to run under load.
If you have a local fixit man, go get a good tuneup for the season. If you do not have a local fixit wizard, try to buy and install your own carb rebuilder kit. There are probably several you-tube tutorials on your specific mower or engine or carburetor. However do not worry, as a lot of the small carbs have similar components and operate the same basic way. Additionally, do not worry if you have extra parts in your rebuild kit as some kits are sold generically and contain parts that may fit in a great number of carbs.
Gasoline these days contains ethanol, which gums up carburetors as they sit in the off season. Sometimes chemicals such as "Stabil" help to alleviate this but not always. A lot depends on how long it sit and how much fuel is in the tank and the carb. Change the fuel in your tank also to fresh fuel.
Hope all that helps,