The joke "Timber" is one of classic Deaf-culture jokes.
A timber man in the woods cut a tree one by one. He yelled "timber" each time before the tree fell down. Then he came upon a tree that did not respond to the sound "timber". He tried again and again. In desperation, he called a tree doctor to come and inspect. The doctor found that the tree was Deaf. The timberman contemplated what to do and got the idea. He called the Deaf timberman for advice. The Deaf timberman said, "No problem. What you need to do is to fingerspell 'timber'." As he fingerspelled "timber", the tree fell down.
Note on cultural appropriation: This joke is to be told by Deaf people based on their Deaf humor, experience, history, and heritage. It's not appropriate for hearing individuals to tell this joke themselves.
On an additional note (January 2021), I watched the video for the first time in a decade and was surprised to see a different version (specifically Deaf timberman) from the "Timber" version in the Signing Naturally textbook! I created this version based on a memory I had from watching my Deaf teacher Sue Bailey in my junior school year. After ten+ years of teaching ASL beginners course and showing the version of the Signing Naturally, I eventually completely the other version until I watched my video above. How precious to preserve a variation!
Q: "I was looking for information on the Deaf joke "Timber", specifically its origin, and how it was spread around?" -- Source.
A: Oral storytelling has been one of the natural occurences in Deaf culture that stories have been passed on from generation to generation, especially before the Internet days. Before the Internet emerged in the 1990s, I had heard this classic joke and several other jokes from my Deaf teacher, Sue C. Bailey (1949-2016), at a school for the Deaf when I was kid. In turn, Sue once told me she heard this joke from her Deaf father. So, this must be very old joke of over 100 years old! So, there seems to be no record of its origin. In my generation, this joke was well-known in close-knit Deaf community across North America through Deaf schools and Deaf clubs.
See a joke: Birds on the Telephone Lines