I have done the following:

1) be patient and wait for it to expire since it was an excellent shot.

2) Shoot again. This will waste more meat.

3) Bull dog the deer and slice its thoat since it was a complet pass though. I did this in my
younger days and had the living ba-geeus kicked out of me at times with the hooves and
racks and even the knife thrown from my hand on one occassion.

Every situation is different and you use what is applicable in that particular situation. Sometimes it ain't always pretty.
As far as the deer looking at you, I'm not even going to go there. Bobby