The first problem I see is you took a gun hunting that you were not even sure was accurate or sighted in. Accidentally putting one round in the bullseye does not constitute a well tuned hunting rig
. I'm not overly surprised you missed deer with it.
Like some of the others have said, you need to shoot at least three shot groups when sighting in or seeing how well a particular load will shoot in your gun. Moving the scope after every shot will not get you very far if the gun and that load do not shoot consistently from shot to shot.
Could it be your scope or mounts, sure it could be but you will never know if you don't shoot some base line groups first to find out what the rifle will do.
Even a load your particular gun doesn't like should shoot 2 or 3 inch groups off from a good rest at 50 yards. So I would start there. Pick a load that should shoot well out of your gun, like don't pick the heaviest bullet you can find, or the lightest fastest bullet they make in that caliber. Pick something in the middle with a decent hunting bullet from a well known manufacturer. I prefer winchester and federal myself.
If you question the scope or mounts pull them off and start from scratch making sure everything is solid and square. Or you could take it to a shop and have the scope mounted and bore sighted. There are tests you can do to a scope to check for proper tracking and the such but you have to know where the gun shoots first and what sort of groups you can get out of it. A shop could check it out for tracking with a bore sighter most likely if you really suspect that.
You can shoot the gun off from the hood of a vehicle with a feed bag if you want, as long as you can hold the gun steady enough and repeatable shot after shot. I prefer a bench or table with an adjustable rest myself. You can get one of the plastic Bench Buddy rests pretty cheap.
Here a few tips for you to start out with. First clean the gun well before you go out. When you get there fire a few shots to foul the barrel out. Some guns will be a bit off for the first shot or two out of a cold clean barrel. When you are shooting groups let the gun cool in between groups. Shoot three or four rounds, then let the gun sit for a while with the action open.
Look for a target or make one with a square bull, not a round one. This way you can line up the cross hairs on the edges of the square instead of trying to hold them in the middle of a circle. It is much easier to do. And for now you really don't care where the bullets strike, just how well they group.
I suggest setting the scope at it's lowest power, especially at 50 yards. The more magnification you have the harder it is to hold the gun steady and the more problems you will have parallax.
One thing you can check is that your scope will hold parallax. Set the gun in a steady position so it will stay still without you holding it. Look at a target 50 to 100 yards away and shift your head from side to side and up and down. In most cases the cross hairs should stay on target. If the cross hairs move around when you shift your head the parallax is off. This means if you don't put your head in the exact same spot every time your bullet could be off by that amount. Now fire a shot and check it again. It should be the same. I have had scopes that would change after shooting them. If this happens your scope is junk and you need a new one.
When you actually start to sight in your scope only aim at and adjust one axis at a time. Don't shoot for the middle of the bull and adjust both turrets. Like if it shoots 3 inches to the right and 2 inches high don't crank on both turrets and then fire another group. Work on one axis at a time. I like to start with elevation myself. Either aim at a square target like before, or draw a line across your target. Aim at that line only concerning yourself with keeping the cross hair on that line. Don't worry about if it is moving from side to side, just try and hold steady for the up and down part. Fire three shots this way and see how far off they are.
Then adjust ONLY the elevation turret the proper amount and try again. When you get the shots as close to that line as you can do the same thing but with a line running from the top to the bottom of the target. Only concern yourself with keeping the cross hairs steady from side to side now, let it drift up and down if it wants to. Then adjust Only the windage knob. After you get them both adjusted try shooting for the center of the target.
Now you can move the target out to the distance you want to zero your scope at and adjust the elevation to that distance. Your windage should be pretty close, but if it is a calm day and needs some fine tuning you can try it. If it is windy out I wouldn't mess with it.
Keep in mind you can only sight a gun as well as you shoot. I tell people the same thing when shooting a bow. You can't tune better than you can shoot. If you are not capable of shooting better than 3 or 4 inch groups don't expect the gun to magically be able to shoot better.
Have someone watch you shoot as well. They can often see form errors or trigger panic problems you don't think you have. Or have someone load your gun for you and let you shoot it. Except have them not put a bullet in every now and then. This will let you know if you are jerking the trigger. Just remember to take your time and not get frustrated. If you get tired or frustrated quit for the day or for a while. It will only get worse if you keep going.
After you get it sighted in off from a bench try shooting it from different positions like off hand, kneeling and prone to see if anything changes or how well you shoot it.
If you have any other questions let us know.
Paul