At a wild guess, I’d think somewhere south of five minutes. The way you would calculate a concrete number is to divide ~2.25 liters by the volume of blood lost per second. That should give you the answer of roughly how many seconds your character can survive. Again, if it’s over 300, I’d be surprised.
There’s a minor issue in that calculation; the blood loss wouldn’t be completely
linear, and if you really wanted to do the math and get it just right,
you could use their blood pressure, and use that to get the volume of
the first couple spurts. Remembering that blood pressure drops as you spray blood all over the place like a broken lawn sprinkler; but even at low pressure, a wound like that is going to loose blood fast.
This is also why I can’t tell you exactly how fast your character will be losing blood. The answer there is “very,” but that doesn’t really help for a calculator.
That 2.25l value is actually an average. The real target is the victim losing ~40% of their total blood. For an average adult male, that’s going to be 2.24l. But, because all of these values are relative to the size of the victim, the time to bleed out shouldn’t be affected by this. There are a lot of medical conditions that can affect bleed times, and recovery. But, I’m willing to go out on a limb and say, at these volumes, none of them will really matter much.
The Wikipedia article on Bleeding should cover you for identifying the symptoms. It has (at the time of writing this), a copy of the four hemorrhage stages. The very short version is that the victim will become cold and clammy, disoriented and confused, unconscious, and dead, in roughly that order.