According to Hiccup in "Snotlout Gets the Axe", he lost both his arms in a "freak mutton accident."
Chosen by Spitelout Jorgenson in Snotlout Get the Axe, he was the third choice for carrying the ceremonial axe, meaning he is most likely an influential member of their house. However, Spitelout claims that Griplout "just couldn't get a good enough hold on the axe with his teeth." This shows that he is almost certainly that he uses his jaws to grab objects as to replace his missing arms.
Later, when Snotlout is proving difficult in getting the axe to the Island of Friga, Astrid jokes that Griplout might still be an option for the task.