A rotary lawn mower is an effective way to chop leaves into small pieces. If you let them fall onto the lawn, the smaller pieces will fall between the blades. You may have to run the mower over them more than once.
Leaf fragments will not harm the grass if the quantity is not too large. They will be gradually broken down by worms and micro-organisms and the resulting humus will improve the soil.

You can also use the grass catcher to pick up most of the leaf fragments along with grass clippings and use them to improve soil in other areas of the landscape. There is typically about a 3 to 1 ratio between leaves raked up and mowed leaves. You will have about 1 bag of chopped leaves for every 3 bags of whole leaves. Leaves can be chopped up with a mower no matter where they fall. You may have to rake them out from behind and between shrubs and flowers.

I also run a lawn mower over dead annual flowers and vegetables after frost kills them or they are through being harvested. The finer you chop them, the more quickly they will break down into humus. They can be immediately incorporated with the leaves into the vegetable garden and flower beds. It is all right to leave them on top of the ground until spring, but fall tilling or spading is better. Fall is also a good time to incorporate bark, compost or other organic matter into the soil.

Organic matter improves soil more than sand, topsoil, or any other amendment. If you have a heavy soil which is hard to work, the organic matter makes air pores so water can flow easily into and through the soil. As micro-organisms and worms use the organic matter for food, they produce sticky, glue-like compounds which aggregate soil into small particles up to pea size, which then act like larger particles. If you have sandy soil, organic matter has the ability to hold water and slow down its movement through the soil. Organic matter also holds onto nutrients so they can be absorbed by plant roots before they leach below the root zone.