I saw this on Youtube at some point in 2020, after having watched The Old Guard with a clip being presented as an example that it was not an original idea. It possessed a similar concept to The Old Guard with there being a small number of immortals, and that they were being chased by people (corporations? governments? the rich?) to be studied for the secret to immortality. The clip shown involved an approximately middle-aged Caucasian man wearing round glassess, and with either a hat or short hair, who's being shot with tranquilizer darts, with him neutralizing one of the darts that hit him on his forearm by chopping his arm off (with an axe?) while bracing it against a wall, only to be hit with more darts. For some reason, my mental image of him makes me think "carpenter", although I'm not certain why.
The animation had the somewhat muted colors that I was used to seeing in anime in the 90s (although, I think that was, in many cases, the result of tapes copied multiple times and becoming more faded with the copies). The people were not cartoony, but neither were they photorealistic, with shading being fairly simple.