Should you chop or shred compost?

No, for compost; perhaps, for compostables. Composting is the process. Compostable materials are what's eligible for the composting process. And compost is the end result. Successful composting requires subjecting eligible materials to proper levels of air, moisture, and temperature; and to regular turning. If composting follows proper procedure, then compost is dark brown, fresh-smelling, organic matter-rich particles that doesn't need to be made any more finer than it already is. Likewise, compostable materials may be placed as they are in the compost bin, box or pile. But the larger materials break down faster in smaller pieces. And so you may choose to chop, cut, segment, or shred compostable materials that take up more composting space, and possibly therefore more composting time.