I think it's unlikely the mat would be causing nicks in the blade. Are you examining the blade before you put it in the cutter? That way if you are sure the blade is not nicked going in, you know that it is being nicked from the cutting. I assume you can see the nick in the blade when you take the blade out of the cutter?
In my experience, it *is* possible to nick a blade on the ruler. When this happened to me, I realized I was not holding the rotary cutter properly when cutting. I was angling it in towards the ruler instead of holding it straight up and down.