In all honesty you have most likely gotten a lemon. I have owned about 6 of the MK/93's in all the variations over the years and have had no issues like you have said. I have read about other people having issues similar to yours.
Why don't we start from the beginning.
Number 1 issues is bad accuracy. There are multiple things that can cause accuracy problems. #1 is usually the shooter, #2 is the barrel. After that you have more in depth items that can cause the problems. Sloppy action (bedding), heavy trigger, sights/scope.
Start with the cheapest/simplest test.
Have someone else shoot the rifle, this may sound like I am insulting you but I am not. When you get frustrated with something that does not work correctly you can skew the results.
Try a lot of different ammo. Don't go cheap. I myself love the Zappers but I use the CCI Blazers as they are always consistent and decently accurate, buy a box of Wolf MT if you can. Cheap ammo will shoot cheaply.
Go through the sights and make sure they all are tight and working correctly, and make sure the scope mounts are inline and tight. Savage rimfire mounts are the biggest joke around.
Release the pressure of the take down screws. Screw them both back in so they are snug but not tight, tighten the rear to 15-20 inch pounds, then tighten the front to the same. If you do not have a in/lb wrench put your finger on a scale and get an estimate of how much that is, only about a pound and half of pressure.
A bit more in depth.
Check the crown. Put white out on the end of the crown to check the muzzle blast pattern. It should look like this. Nice and even. If it does not you may need to polish the end. It is super easy and cheap. All you need is a screw gun, polishing compound, and a round headed brass screw. Chuck the screw in the screwgun, smear it with polishing compound and stick the screw in the muzzle for a few seconds. If the crown is not to bad then it will polish away any imperfections. Clean it good and reshoot. I did this with a friends 93wmr and it really cleaned the groups up, helped a lot.

Check the action/barrel. Yours is wiggly but I don't know how much that will effect the accuracy at that short of range. Make sure the barrel is fully floated. You have a wood stock so if the barrel is hitting the sides you can either sand out the channel or if there is a lot of room you can hog out the action and bed the rifle so the barrel is aligned correctly.
Lets got the easy way first. Wooden dowel and sandpaper to sand out the barrel channel, don't worry about the action. Take it slow and do it right. When it is floated reshoot.
If it still does not work you have two choices. Easiest is to call Savage,
http://savagearms.com/contact.htm, tell them what the problem is and see if they will check it out. This is the easiest, cleanest, and slowest method. You can do this at any stage of the process, preferably after you have done all of the non invasive procedures.
Second choice is to bed the action, might as well pillar bed it. If you are not comfortable with going this far into your rifle any competent gunsmith can do this for you. If you are adventurous or brave, I'm just plain to dumb and cheap, you can do it yourself. It takes a couple of days but is well worth it.
http://www.6mmbr.com/pillarbedding.htmlAfter that if it still does not shoot, go to your local smith, have him get hold of Savage and take it from there. Then go purchase a CZ