If not bleeding out then let it bleed a bit to help flush out contaminants. Then pressure to stop bleeding and cover it to help keep clean. Finish taking care of your deer then go to the ER to get it flushed out and stitched up.
Throw some peroxide on it, apply pressure to stop the bleeding, doesn’t look like it needs a TQ. Then drive to the hospital, will likely need a stitch or two.
Clean both with water or saline. Irrigate ifyou can. 1 or 2 stitches up top or super glue. Gauze. Bottom gets 1 stitch and covered with gauze. compression wrap and check every hour for 4 hours tomake sure the bleeding stops. if it's notstopping getting worse, use a tourniquet and get to a hospital or biganimal vet. The bottom stays open to drain dirt/ infection. go to a regular MD if bleeding stops or slows whenyour schedule allows
on a bwca trip with 3 guys [game wardens] one of them was cutting fire wood with a hatchet and sliced his leg good. we were miles of paddling from any help. i had surgical disinfectant to mix and clean the wound. then duct taped it up good. i dont think he ever went to the doc. at least we drove home to arkansas before he did.
so far that is the only severe injury encountered on backcountry trips.