I am right hand and if I pluck or otherwise get a sloppy release my arrow tends to go right. For left shots, I think it most times is my bow arm or bow hand. Best thing I can do for left shooting is be sure to have an non torque grip, be pushing on the shot, and not be at full arm extension at the shot so my arm can only follow through by going left instead of straight ahead. I also find trying to hold the bow with no push can cause my arm to jump around on the shot.
Another left shot issue for me is not getting my anchor tight into my face or pulling through tight to my face. Getting your fingers sticking out farther or the face mask could cause you to hit anchor, but have your string out a little and throw your shot left.
There are many other factors like panic on a deer, but you said your arrow went low and left on the deer, and it was doing that off and one while shooting the target. Deer panic usually cause shots to go all over the place not on consistent spot. Could be a combo of stuff, but I suspect something in bow arm or anchor.