Cool video. I'd like to work with that fellow. I've never tried to cut a tenon only with an axe, but why not? I'll give it a try.
The way I do it now requires saw, axe, mallet, and slick.
handsaw shoulder, align edge of axe with cheek line on endgrain and whack with mallet. Score cheek lightly with axe, finish with slick.
It goes really quick, especially in straight grained stock.
Whit

There is another 'axe' not mentioned here that is extremely useful for the cutting of tenons and mortises, a tool that is used extensively into modern times in those regions of Europe that ever came under German influence, which is pretty much all of central and western Europe. This tool is the German Stossaxt, also known as stichaxt


This tool lies somewhere in the strange world between the felling axe and the framing chisel, and it leads me to suspect that the chisel itself is descended from the axe.
The French Besaigue is a very close relative of this tool, descended from it I believe. t is essentially the same thing, only with a mortise chisel added to the other end.

In my opinion, this tool is the best tool I have ever used for cleaning out the sides of just about any joinery, especially deep mortises.

AS I understand it, the hollow handle on the end of this tool once had a wooden handle mounted inside of it, but eventually they discovered that was totally unnecessary. You use the tool by gripping the steel handle in one hand, and holding the body of the tool just below the handle in the other, then pushing it somewhat like you would a slick, but you can also use more of a chopping action should the need arise. This tool is very easy to use, and extremely accurate. I doubt now that I'll ever use a slick again...

Another tool is the German bundaxt

this is a multi-purpose tool that German carpenters seem to put to good use. It is used for notching out when hewing, and for cutting joinery.

Ochsenkopf makes a bundaxt, and Müller also makes one. I plan on buying a set of them sometime soon