"Axew mark their territory by leaving gashes in trees with their tusks. If a tusk breaks, a new one grows in quickly. They use their tusks to crush the berries they eat. Repeated regrowth makes their tusks strong and sharp."
In their battle, Drayden cast doubt on Axew's strength due to the fact he expected that Axew would have evolved into Haxorus, however, Lexi showed Drayden just how powerful Axew was as he led her team to victory battling against Drayden's Haxorus. He then was used in battles against Caitlin of the Unova League and Iris, now the Champion. He rebattled against the same Hydreigon he lost to in their first battle two years prior, in which he won.
Upon Lexi's decision to travel to Kalos, it remained under the care of Hayley, which Lexi said would be good for him so that he can gain independence away from her for a while.
Axew is a very immature and childlike Pokémon, who likes to show affection and be positive. He often clings to Lexi's bag or foot, if he's intimidated or scared. Axew has shown many instances of bravery and strength throughout it's time on Lexi's team, usually when Axew is trying to show himself that he can be. He gets easily upset and frustrated over losing in battle, or when he's not successful in doing something, although with words of encouragement he perseveres.
His relationship with Lexi seems to be similar to that of mother and child, in that Axew treats Lexi like his mother and she like he's a baby. Despite this, Axew has always tried his hardest and best to become stronger and a powerful Pokémon, so he can make Lexi happy.
Axew has weaponised tusks that in the wild he uses to crush berries to eat. Repeated regrowth make them even stronger and sharper. He also uses these to mark territory or to help mark tracks.