Cutting mat that is 12 years old - time to replace.
As for the cutting problem being the cutting mat or the cutter. It could be both!
Sometimes my blade skips threads when cutting. Usually I need to change blades. But sometimes the screw that holds the blade in place is loose. That also causes wavy cuts.
Mat - I notice that I tend to cut in the same place on the mat all the time. Move your fabric to the center of the cutting mat and then cut. You might see a big difference.