I agree with Hissy. Sawdust is so sticky, I think the kitties would lick up a lot of it when they were cleaning there paws, not to mention tracking sawdust all over the house.
It sounds like the wood is from felled trees? If it is from treated wood or plywood then for sure DO NOT USE. Treated wood has poison stuff like copper naphthenate to keep bugs off. Plywood has all sorts of glue.
yeah,i think it depends on what wood it is. but i know that at my local supermarket you can buy woodshaving cat litTer ..i'll have to pay attention what kinda wood it is next time, and at our cat shelter they use woodshavings too. i've used the wood shaving cat litter from the supermarket and i found it controls the smell better than clay litter.