Bloody Tree was added in Beta 30.0. Previous Versions can be found here.
Since Beta 48.1, Bloody Tree has the ability that originally belonged to Shambling Mass: A Magic effect that deals Fatigue DMG to the opponent.
Fatigue DMG is dealt to a player whenever they fail to draw a card. The cause for this is an empty deck or the use of Preservation. This starts at 1, but each addition time it's triggered increases the DMG by 1, and there is no way to reset this counter.
As a result, each Bloody Tree deals at least 1 more DMG from the last, and is a good addition to a mill deck (as causing Fatigue is the main objective of such a deck).