Bah, Horsehockey!
Can't say that I agree with a lot of stuff here.....
You don't lop off tree limbs for amusement with even an entry level katana. They're not designed for that. You'll probably get hurt doing it. Bad idea.
That you would use a Katana for "limbs in the back yard" suggests that you're not ready.
Cheness swords are fully functional - they're designed for cutting and cut they will and do - limbs are no exception and are fine medium to test. You'll hurt yourself if you're stupid; you won't if you're not. This is true whether cutting limbs, tameshigiri, or riding your bicycle down the street. But OK, point taken if it were a cheap decorative sword - would be good advice in that event.
http://www.chenessinc.com/
These are serious instruments properly forged and heat-treated. Serious enough for serious backyard fun, of any type of the owner's choosing.
As to a katana as a "backup weapon", again not a good choice. The katana is usually too long to swing in the confines of a home.
Well, yes and no - he said "Ko-katana". The Ko-katana or chisa-katana is the short one - wakizashi length, with katana 2H handle. 21" in the case of Cheness products. I have the Cheness 9260 Ko-katana and consider it an excellent home CQB weapon. Well, let's say "very good". A gun is "excellent".
Ko-katanas:
http://www.chenessinc.com/ko-katana.htm
Videos of sword dudes cutting all manner of limbs among other things while testing Cheness and other brand swords (with no ill effects - to themselves):
http://www.sword-buyers-guide.com/authentic-japanese-swords.html
In particular, look at the testing of the "Tenchi":
http://www.sword-buyers-guide.com/tenchi.html
Scroll down to the video.
The "Shura" and "Tenchi" Ko-katanas in 9260, through-hardened, are super tough and sharp instruments - the Chenesses are cheaper because they're not as authentic and decorative as other Japanese swords, in the small parts used.