What DeathChef said, with a bit more elaboration.
You must edit the Harvest (Gold and Lumber) ability that worker units have. In there, you can edit these three values:
Data - Damage to Tree
Data - Gold Capacity
Data - Lumber Capacity
Set the Damage to Tree value to some ridiculous height (like 500) and your peasants (or other workers) will chop the tree in one go. Also, set your Lumber Capacity higher so that they can carry all the wood. I'm not sure what the "health" of trees is though, which would be handy to know if you want them to carry exactly one tree.
By the way, if you still want other workers to be able to harvest normally, you can make a new ability like Super Harvest (Gold and Lumber), and make your "super workers" use that.