If you want a quick way to get wood, look no further than the beaver dams. There is so much wood there and there's also cementing paste and rare flowers/mushrooms (sometimes silica pearls too!). Although the beavers can make this tricky...
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.
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.
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.
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)_/¯
2 man Meta : Someone chainsaw trees and the other guy is punsh him from tree to tree when u have full cap of wood the other guy can grapple u to the base (grapple tipp: try to grapple on head idk why but it worka better)
If you have a mammoth and a chain saw you need to use them in conjunction for gathering I could get almost 800 wood per tree now my chainsaw was ramshackle though but it was easy to carry 3,000+ wood makes behemoth gates as sinch!