I used to be an EMT and in an area with a higher than normal amount of medical doctors. I had two calls where the doctor was a neighbor and showed up before I got there. First thing, as George said, they don't have bags. Second is they let me do my thing and stepped back. My job as an EMT is to get the patient to the hospital where they actually have equipment and lots of trained personal. Smart doctors understand that, know that we know what we've got on the ambulance, and by and large, leave us alone.
For an EMT, this is simple. Secure airway, apply pressure to the wound to control bleeding, large bore IV if there's a paramedic, O2, and prepare for the crash. Then get to the hospital as soon as possible. Race is between whether we get to the hospital first or the patient bleeds out first.
Suicide is not an issue for the EMT, other than the patient might be refusing treatment.
As patient bleeds out, lower and lower level of consciousness. All we can do is slow the bleeding as best we can. And tell the driver to "GO!"
Best of luck,
Jim Clark-Dawe