For pretty much anything I want to shred, from dry leaves and grass to green twiggy holly bush cuttings, I shred with a rear-discharge lawn mower with a bagger. Use (generally) in 2 ways:
Way #1. Coarse shred: with the bagger attached, and material to be shredded spread out, make a single pass over the material until the bagger is full. Empty the bagger (into a bin, etc.) every time the bagger is full. This is perfect for shredding fallen leaves mixed with grass into a good weed-supressing mulch. Also fine as compost pile feedstock.
Way #2. Fine shred. Type A: You can start as with Way #1 but don't bag in the first pass. Essentially just mulch it onto the lawn. Then, attach the bagger and go over it again; this will bag the fine mulch but also leaves some on your lawn. This makes a finer mulch that breaks down somewhat faster during composting. Type B: if you are mulching green twiggy cuttings (such as green boxwood, privet or holly cuttings) make 2 passes over the material, bagging the second time. you may need to rake up some woody bits to bag separately for municipal greenwaste composting. This mulch adds both green and brown material to your composter. Type B also works for big tough weeds that require a lot of chopping up.
I don't bother trying to shred larger woody materials. I leave such material for municipal greenwaste collection and composting.