Raider,
To be honest Tenshin Ryu is a school of japanese militairy stratigy founded in the 1700's from Katori Shinto Ryu. It teaches all disiplines needed to perform as a samurai in the warfare of that time.
Karate as you think of it is a modern invention. Atemi wasa, striking techniques, have existed as part of armed warfare since it's inception. Testing ones ablility to perform the techniques of striking an opponent or cutting an opponent is standard fair for your education in such a school.
Testing your strikes, tamashiwari, could be on wooden boards, bricks, rocks, cinder blocks, ice or killing animals in a slaughter house. Testing your cutting abllity, tameshigiri, could be on green bamboo, green wood, rolled up grass matts, and as a freind of mine would do, purchase a fresh killed pig carcass. It is very close to a human body in density and structure.