I would not run over cardboard with my mowers. Wet it might be soft enough but I would not want to ruin the blade or knock it loose.

I run cardboard through a regular paper shredder. Mainly it is for bedding in my worms bins. I have a cheapie paper shredder that is designed to shred CD's and credit cards, so cardboard is not a problem. I just use a box cutter to cut cardboard into 4 or 5 inch widths and then run it through. I get small pieces.

store it outside and near your pile----let it get wet from the rain and shred it by hand-----

Therapy for the soul===

JB

I run over cardboard all the time with my lawn mower I have no idea how paper could damage a steel blade If you had a bagger it sure would make short work of it

Most of my cardboard goes in the pile whole about a pickup load a week from the shop the boxes my dog drags into the yard to play with get run over and mulch mowed in place but them sticks don't scare my lawn mower either

Nice soaking rain all day Monday----- got home and stood in the dark in front of my bins shredding DW's wine boxes--

--just a nice misting rain at this point and the boxes shredded with ease ---- about 10 minutes of quiet ---just me and the mist and the bins

therapy for my stressed out brain ----JB

Joebob that is a nice image, I can almost smell the misty rain

You've got a tap handy for the pile, just sprinkle the cardboard and tear it apart.....easy.
No, I wouldn't suggest you use a lawn mower -- I would think it could grab under the deck and who knows what might happen. Mowers are designed to cut grass, not boxes.

I save the better cardboard boxes until I have a bunch, then I offer them on a Freecycle and someone always wants them enough to come and get them. Cardboard boxes are in such high demand that people even ask for them on the Freecycle.