After the death of Eugie, Arnold acts like a stone for several reasons. The first of these is that he does not want to draw attention to himself in any way. Perhaps he feels that by melting into the background his parents will forget about him; thereby also forgetting what he did. Also, there is not much emotion shown in this family prior to Eugie's death, thus, Arnold has no real experience showing emotion. Finally, each person deals with death in their own way. Arnold is personifing the "hard scrabble" way of life associated with life in the country.
Another reason Arnold acts like a stone boy after Eugie's death is that he is in deep shock; he has just experienced a traumatic event. At nine years old, Arnold struggles to process the impact of his actions. Like many victims of trauma, Arnold falls back on shock and denial as a response. He commences picking peas calmly, as if he hasn't a care in the world.
Upon closer examination, however, the reader realizes one thing: Arnold is cognizant of the fact that his brother will never wake again. However, Arnold is so severely traumatized that he can scarcely feel anything. In fact, he doesn't feel the numbing effect of the cold pods "until some time" has passed. Victims of psychological trauma often resort to emotional detachment in an effort to inspire some sort of emotional equilibrium in their lives. Arnold essentially becomes a "stone boy." He resorts to this coping mechanism in order to deal with his grief.
We can see evidence of Arnold's emotional detachment when he coolly announces Eugie's death to the rest of his family. Later, when the sheriff questions him, Arnold's answers are short and blunt. Again, he shows little emotion, and the sheriff concludes (unfairly) that Arnold feels "nothing" about Eugie's death. The sheriff's assumptions cause Arnold to question his own sanity and humanity.
We can see the dramatic irony here: Readers know that Arnold isn't the unfeeling boy everyone concludes he is; he is merely so traumatized that he has difficulty processing his feelings. However, none of the other characters in the story seem to understand this. Arnold's family keeps him at arm's length, while the sheriff rejects any idea of Arnold being sorry for his actions. Additionally, the neighbors express little sympathy for Arnold.
For his part, Arnold tries to approach his mother in the night in order to pour out his grief and terror. However, he finds himself rejected and humiliated. In the end, Arnold receives no comfort or solace from his mother. Later, he frightens even himself at his own lack of emotion; essentially, he goes back to being a "stone boy" in order to maintain some measure of self-respect and sanity.