This is something I talk about frequently in the dojo. It can be very controversial. My Sensei has discussed this at length, and so I share what he teaches. Mat cutting (Tamashigiri or Shizan) was developed as a way to test the sharpness of blades. It is not how sword masters used their blades to make cuts in combat. This Kensei (sword saints) in particular would not have cut with their swords the way mat cutting is done. But don't just take my word for it, or the word of my Sensei. Watch this video from the Soke of a completely separate Japanese sword system, but one that is quite old like our system is. This level of understanding is not found in martial arts (really martial sports) developed in the modern age.
Shane Sensei is a licensed Shidoshi in the Bujinkan and member of the Shidoshi-Kai. He has trained in the Bujinkan since 1998 and regularly travels to Japan for training.