As a mage, I would normally use Crushing Prison or Gravitic Sphere to disable a single strong melee enemy. But the Arishok seems to be largely unaffected by Crushing Prison, and he is able to use his charge attack to escape from Gravitic Sphere instantly even when he is at the center. Even kiting doesn't work very well because of the charge.
Perhaps due to spell choice, it may be impossible for this mage to beat him, but how would some other Hawke do it?
Best Answer
There's a nice strategy guide at Dragon Age wiki, section Mages, including some ideas and observations on how to beat the arishok, which spells to use and how effective they are.
It's been some time, but as far as I remember I managed to beat him with a combination of immobilizing spells (Cone of Cold, Winter's Grasp, and I think Crushing Prison worked most of the time, too), (any) damage-dealing spells available when he was unable to move or too far from Hawke to attack, few Heal spells (only needed them once, maybe twice), few Lyrium potions (which you don't need if you watch your mana pool during the fight and choose spells carefully) and some running around -- it wasn't hard to dodge his charging attacks.