To get wood, use normal attack which is slashing with claws. To get berries, use bite attack. To use bite attack on mobile, change multi tap to alt attack 2 and tap with 2 fingers when riding the Therizinosaur. To get fiber, use the tickle with claws move. To use the tickle with claws move on mobile, jump when riding the Therizinosaur.
Best tame for gathering hide. Level heavy harvesting, and use C attack (bite) on corpses. It harvests only hide (and lots of it) from most dinos, so your inventory won’t be clogged with meat and whatnot. Nothing comes close to this efficiency for gathering hide.