A system for cutting blocks of cheese or other food product into chunks includes conveyors for moving the blocks along an automated, continuous, in-line processing path. A block cutter cuts the blocks longitudinally and or vertically to provide one or more stacks of slabs which are destacked by a vacuum transfer apparatus. A transverse cutter cuts the individual slabs to create chunks of cheese or other food product. The conveyors include a stack conveyor located in the processing path for conveying successive stacks of slabs from the block cutter to the product destacking apparatus in succession, and a slab conveyor located in the processing path for conveying successive slabs from the product destacking apparatus to the transverse cutter. A trim cutting module includes a rotating mechanism that rotates a block during the trim operation, allowing trim to drop to a trim disposal conveyance.