As mentioned, make sure that you have only one blade in your cutter. Then make sure that you have reassembled it correctly. You are not supposed to tighten the screw down all the way on some cutters. If you are using a HF blade, you might just have a bad one. I have had bad luck with them.
Yes, mats do wear out eventually. If your mat is wearing out it's usually because of repeated cuts in the same area so you will most likely have skipped cuts, not a difficult time cutting in general. If you tried the back and are still having problems I'm guessing it's not your mat.