Even though Casteroids are better at collecting wood, mammoths can carry so much more, and have higher weight reduction. They also move faster and have a larger attack range. When gathering wood on a mammoth, I personally have found that it’s stomp, or left trigger (Xbox) attack gathers more than its main attack

Although they don't have weight reduction Theris are extremely fast gatherers. I gather wood with my Theri and have a beaver following so that when my Theri gets encumbered I just throw it all on the beaver.

Beaver dams in the rivers have wood

Go to edge of redwoods, hit the tall redwood trees with chainsaw and you’ll get a lot doing that.

I would recommend taking something what could withstand the weight

Therisinosaurus collect wood very fast and very effective, but with it it becomes encumbered very fast too. Mammoth collect it not very fast, but it has big radius of attack and it can takes large amounts of wood with its high weight and weight reduction of wood in its inventory.

A note on Mammoths and Wood. I have recently noticed that mammoths seem to be less good than Castroides at getting wood, HOWEVER, I then realized... For whatever reason, if you want Mammoths to get mostly wood. The "attack" they use is the [spacebar]... I never would have thought of that, but what do you know! ¯\_(ツ)_/¯

You can use a stegosaurus to gather woods, using the heavy plates mode. They don't have weight reduction, however, they have a lot of weight. Moreover it gathers so much wood! It's amazing, I have a stego named Stella and every tree give me almost 100 woods and she can hold between 800 to 700 woods inside it's inventory.

For mobile,u can’t farm wood with Stego.

Enable Moschops wandering and they will collect many wood with berries and thatch also

Take mammoth to the swamp on any map you'll get tons of wood plus the added bonus of rare mushrooms and flowers