I'm having a tree cut down next week and it is dramatically cheaper if I haul the wood away myself. I posted an ad on Craigslist advertising free wood if the respondents cut and hauled it away themselves. The tree service recommended I not allow others to operate chainsaws on my property for liability reasons, which is very understandable. If I had these people sign a liability waiver, would it stand up if something were to happen?

The issue will be your relationship with them.
Are you "hiring" them to cut the tree for the value of the wood. If so they are working as unlicensed workers, and you may be liable for any injuries on the job.

The issue with waivers is that you will not know if they stand up or not, till you are sued.

The issue with waivers is that you will not know if they stand up or not, till you are sued.

Liability waivers are not a perfect fix. But they can help avoid a lawsuit for at least two important reasons:
1. The people who sign the waiver will be reminded of the danger and hopefully be more careful.
2. They might not sue if injured because they are disuaded by the existence of the waiver.