So I have had both Savage Mark 1 and Mark 2 rifles and had this issue with all of them. I currently have a Savage Mark 1 FVT and after 300 or so rounds this issue reared it's head again. With certain shells (the ones that are most accurate) it will fail to extract them. Basically the extractor just bounces off the rim of the casing and I am stuck digging the empty out with my pocket knife. This is super annoying. My google searches revealed this is a very common issue and there are about a 100 ways people have tried to fix it, most sounded pretty kooky, such as sanding the chamber so it was loose! I happened across one fix that seemed more resonable though.
The firing pin, extractor and shell guide are all held to the bolt by a spring clip. This both retains them and provides spring tension for the shell guide and extractor. Apparently you can fit another clip over the original one and effectively double the spring pressure for the extractor. So I ordered one from Western Gun Parts and with some playing around last night I managed to get it to fit. It is still smaller than the bolt so you notice no issues cycling the bolt. The extractor is very hard to move now (before I could pull it out with my finger). I pulled the bullets and powder from a few cases (safety first!) and cycled them through the chamber, they extracted great! Now I just need to try it with live rounds, but before adding the other spring it would not extract my dummy rounds, so I think it is good.
Just an option if you are beating yourself up trying to shoot you Savage. I like everything else about the rifles, just a terrible bolt design.