Can I cut up sheets of cement board and use it as wall shingles?
Cement board and fibercement siding (such as that from GAF or Hardie) are very different things. I'd never have considered cement board as an exterior product, especially in a climate with severe freeze/thaw cycles. I'd expect it to simply disintegrate as it'll absorb moisture readily. 

Also, to cut that into siding shingles would be a monumental task, generating huge amounts of carcinogenic dust and burning through a good heap of blades.