I learned the hard way that there are really only two kinds of injurys.
Stuff you can either ignore or put a Bandaid on if it makes ya feel better, and real injurys that involve stemming blood flow while waiting for an ambulance.
Most 1st aid kits are booboo kits.
Kotex pads(Mickey mouse Mattresses) and duct tape, and hand towels and duct tape staunch blood flow and ya can stack them as they soak through without releasing pressure on the wound.
Save all the fancy sterile crap for the doctors and emergency rooms.
If the guy or yourself manages to make it there, one of the first things the doc is gonna do is pump the victim full of antibiotics and debride the wound of saw chips, fibers, and other crap anyway....after they cut away the tissues that ain't gonna heal.
All I can add is cussing a blue streak while trying to stop arterial bleeding with your hand, cuz there is no band aid in the kit big enough, sucks.
Folks bleed out quicker than most think.
I keep 2 Motel towels and duct tape as a kit nowdays.
Vehicle accidents and saws tend to involve more than just booboo's.
Good topic.
Stay safe!
Dingeryote