I’ve seen this in the show Scorpion on CBS, and they used this trick (when the wound was very large with lots of blood loss):
That is called cauterizing. It “fuses” the skin back together to create a nice closure between the torn areas.
Someone with surgical skills or experience performing it should cauterize wounds on the go, but it is a working tactic that should only be used as a last resort due to the non-sterile conditions involved.
The “biting on a cloth” thing isn’t just to restrain movement…it’s a pretty tough addition to this. Imagine setting all of your skin tissues on fire individually. LOADS of pain. You’re probably going to have spasms as the intense pain travels through you, but by biting down on something, you’re channeling the pain to a controllable source of pressure, thus offering a slight reduction of discomfort.
(I know nothing about medical attention, but this is what I heard from the show - which is about 90% accurate)