Why does my mower shutoff and backfire when the blades are engaged?

@fffexzmelpacryh those symptoms are usually caused by the air fuel mixture not being correct. Once when a load is put on, like the blades are engaged, the engine will die. I would start with the fuel lines, fuel filter, and new fuel. After that, it might be time to pull the carburetor apart and clean the jets, float valve etc. Replace any carburetor gasket that seems to be damaged, leaking etc. The other thing to check are the plug and the coil. Make sure that those are cleaned, replaced and checked. For more specific information we would need to know the engine make and model. The commonly used engine for the D105 was the 17.5Hp Briggs & Stratton single cylinder 31G777 gasoline. Let us know if that is what your mower has.