Well, injury to the carotid artery is survivable provided immediate (i.e., within seconds) efforts are made to control the bleeding. Ask former professional hockey player Clint Malarchuk, who survived just such an injury when another player's skate slashed open his internal carotid artery during a game. His team's trainer, a former army medic, pinched off the wound and bought him enough time for doctors to come and suture it. I'd say it's within the dwarves' level of medical capability to manage that kind of injury, at least in the short term, provided they reach the wounded in time to treat him and then do so right there in the field, as opposed to dropping him off in a hospital first.
They teach "blood chokes" and other nifty moves...if you choke someone properly they can go unconscious within about 3-6 seconds of no blood to the brain and can die in about 8-14 seconds
The first part is 100% true. Once you cut off the brain's access to oxygenated blood, it doesn't take long at all for the person to pass out, as opposed to an air choke, which can take quite a bit longer to work and is also potentially more deadly even when properly applied.
The second part, though, is not necessarily true, although obstructing blood flow to the brain for longer than a few seconds at a time can cause brain damage; the longer the duration, the more damage that is done.
I've heard about dying from holding the choke for about twenty seconds before, but never thought about it much. I looked it up, and I think it's called "carotid sinus reflex death". It's actually not universally accepted as a mechanism of death. Supposedly, strangling the artery can lead to a particular nerve being stimulated that leads to cardiac arrest.