You cannot use makeContrasts() to make a contrast for levels that don't exist in your design. And writing dummy code that cannot possibly work isn't a useful thing to do, because, well, it won't work, so what's the point? You are much better off trying to say what you want using words rather than fake, wrong code.
Also, don't respond to answers with another answer (you are not answering anything). Use the ADD COMMENT link at the bottom of the answers if you want to clarify something about a previous answer.
So, back to the story. An unpaired t-test is exactly analogous to the SAM two-class unpaired test, so I am unsure why you think they are different (just as a one-way ANOVA with only two levels is identical to an unpaired t-test).
The design you are fitting is a 'cell means' model, which computes the mean for each group (Norm1, Norm2, etc), and which will allow you to make any comparison between any of the groups. So you can compare Norm1 to Norm2 or Norm1 to Mut3 or whatever. The underlying assumption would be that each of these groups is somehow different from the other groups (e.g., the Norm1 and Norm2 samples are both normals, but somehow different as well).
If you want to do a contrast of Norm - Mut, then you have to first fix the colnames of your design matrix, which will be
 "AF.groupMut1" "AF.groupMut2" "AF.groupMut3" "AF.groupMut4"
 "AF.groupNorm1" "AF.groupNorm2" "AF.groupNorm3"
> colnames(AF.design) <- gsub("AF.group", "", colnames(AF.design))
 "Mut1" "Mut2" "Mut3" "Mut4" "Norm1" "Norm2" "Norm3"
As I mentioned in my first answer. You can now create a contrast matrix using those names
> makeContrasts((Mut1+Mut2+Mut3+Mut4)/4 - (Norm1+Norm2+Norm3)/3, levels = AF.design)
Levels (Mut1 + Mut2 + Mut3 + Mut4)/4 - (Norm1 + Norm2 + Norm3)/3
This will compute the average difference between the Mut and Norm samples. Whether or not it makes sense to do so is something you have to decide.