Not from a saw, but a tow rope took the top 1" off my right thumb while water skiing off Race Pt. in 1988.
Surprisingly there was little/no blood, but just the bone, tendons, and nail base were all that was left. Didn't feel much pain, but was a little shocked when I wiped out, righted myself,reached for the tow line and noticed the damage.
It took three weeks immobilized in CC Hospital to establish the skin graft and three cosmetic surgeries to dress it up a little. The only reason we saved the thumb as opposed to amputating it was because the thumb is obviously critical for helping grip things such a baseballs and revolving spool fishing reels.
As for work, I just taped it up and began fishing/working again in about 4-5 weeks but it was sore for a long time and I couldn't put much pressure on it. It did take the better part of two years to redevelop feeling in it. I had to have the nail base removed so theres no nail, but its fully functional now.