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It depence on what you need but the nearest place to do so some groceries is in Madaba.
Its is a nice place too for visiting so beautiful sites and some nice restaurants.

Amman is app one hour drive a way from the Dead Sea so I can imagine that you don't want to do this on daily basis.
But it is the place where you can find a lot of things which is not very common to buy.

Thanks Primadonna for your advice It really helps because I'm just 1 week here in Dead sea and right now I am in Amman processing my iqama I'm planning to visit Madaba, Mount Nebo and Mujib too

easy. . . Rovers Return Pub at the Samara Mall is a good starting point. . . .
there's a supermarket more or less next door. . . small and a bit expensive but helpful (perhaps they can get stuff for you if you ask) . .. we really like Abu Khaled's Tropicana Store just before the barrier, for very basics but he does run short sometimes. . . otherwise the supermarket in Rama by the mosque is good. . .  lots more ideas come back if you want more!