I think [the response give by] Dr. Davis is correct. In general, when you are in a place where you can obtain medical attention LEAVE THE ARROW ALONE (or the knife, or the ……). It could not only be tamponading a bleeding source, but removal – aside from the issue of tamponade – may cause further, and more significant, damage.
But if you are, say in a place with no health care, all bets are off. And there, my friend, you will have to use your best judgement. And this best judgement would relate to the anatomic site of the injury. So, an arrow deeply embedded into the chest is different that one in the thigh; the former more dangerous than the latter.
I hope this helps.