Most cat litter is clay based as previously stated, but high priced, fancy "crystal" stuff may be different. The clay would be a fine abrasive material, but I wonder if the litter would break down into dust or if the material "edges" would quickly become rounded, thereby, losing it's "cutting" ability.
If you feel like experimenting with the litter, then DO NOT add any liquid. Of course we expect a report on the results.
A lack of planning on your part does not necessarily constitute an emergency on my part.