That sword is claimed to cut through anything. I see no reason it can't cut wood.
Also Sugetsu has a Tailed beast like construct. was able to hold killer bee was stated along with this brother to be the 2nd Demon of the Hidden Mist said to be better then Zabuza by Kisame with the carving knife.
Suigetsu has this one in the bag..I don't think Mokuton is do much to someone who can liquefy their body..The only option for Yamato is to suppress Suigetsu's chakra through his mokuton..But since I usually put both of them in the same Jonin tier, I don't think it would be that easy..Hidden mist + Silent killing is a legit problem for Yamato
Suigestu's got this, his durability was able to take a Biju bomb at point blank range which is around mountain busting. Yamato doesn't have that kind of fire power and the best thing he can do is suppress his chakra (wood style's ability is to suppress chakra).