Is it possible to root woody herbs, such as sage or lavender, from cuttings?

It's possible, but not real easy. I've had more luck by layering, not cutting. Just push a stem into the ground; put a rock on it if it doesn't stay in. It will root in a month or two and you can cut it off and make a new plant out of it.

Is it possible to root woody herbs, such as sage or lavender, from cuttings?
The way layering has worked best for me is to take the longest branch from the base of the bush, score the stem not quite to the center (careful not to cut right through). This wound creates an area to heal and in doing so will be where roots are produced. Before covering it up apply some rooting hormone powder (available at Home Depot) to the cut area, then bury that section still attached to the plant and let the tip come up out of the soil again. You will need to leave it there the entire season. Don't nudge it or try to peek to check because the first roots are very fragile and you'll snap them off again. Once roots are formed, you can sever the stem by putting a shovel in the ground straight down to cut it off the parent plant.