The Key to a clean Kill in regards to bowhunting is Practice practice practice. I hunt with a compound bow and most years harvest enough meat for the year before gun season begins so I've seen many different situations regarding what happens when an animal has an arrow stuck through it.
My dad passed on the passion for hunting to me and also forced me to practice until I could consistantly place 5 arrows within a 6" diameter at 20 - 30 yards before I could hunt with a bow. I also had to build up strength to pull back a bow with enough poundage to penetrate and break bones if necessary. Many states require 45 lbs draw weight minimum for Deer which and average man can pull with no problem. after building strength, it's better to go higher incase you do hit bone.
I've shot deer right where you're supposed to (through both lungs and the heart) and amazingly they run 1/4 mile. I shot one deer, hit it in the hind quarter. It jumped in the air, didn't run, and then fell over after about 5 seconds. (hit the artery between it's hind legs)
the vast majority of kills I've made with a bow have been clean kills, but very few (1 -2) have been an instentanious drop in thier tracks.
Your responsibility as a bow hunter is to get enough practice that you can put the arrow into the vital organs of the animal. Depending on the angle this is -for reference -about the size of a paper plate. You also have to have the discipline to not attempt a shot if it's not right. You cannot punch an arrow through a little bit of brush and expect it to go where you aimed.
To hit a pie plate consistantly is not good enough IMO. standing at the range in your T shirt plugging away at a stationary target at a fixed distance is great for building fundementals, but when you are hunting, you'll most likely be cold, in a stand or on uneven terrain, all geeked up on adrenalin, and no matter what you say that deer will not come stand still 20 yards away and wait for you to get ready.
If you can put 5 arrows in a 3 - 5" group CONSISTANTLY from different distances and positions with a bow draw weight of 50 lbs or more, you're ready. That will probably take you a few months depending on how much time you put into it.
Learn the skeletal structure of a deer so you know what can get in the way of a good shot.
There are times when things do go wrong and you have to track. I'll not give the anti's ammunition by going into those situations, but you need to be prepared for that possibility.
So to answer your question, Yes it is very possible to make a clean kill, but you need to take the responsibility to train yourself to do it.
There are plenty of books and videos out there, but I'd suggest finding a shooting club in your area and ask a lot of questions there. I'm sure you'll find someone willing to lend a hand on getting you started.