Deidara found the arm that Kakashi severed:
Kakazu probably sewed that back.
However I am not sure how Deidara got his other arm back. His next apperance where he attacked the Three-tails, was probably only with on arm. It's a little unclear, but his shadow at the bottom row, middle panel showed only one arm:
And then Deidara got both his arms back..
So it might be possible he used someone else's arms or whatever. It isn't that important anyway... since we've since arms pop up of no where in this manga.