The unremittingly factual, unemotional mood of My Side of the Mountain is perfectly in keeping with both Sam's personality and the nature of the story he has to tell. In recounting the tale of his numerous adventures in the Catskills, Sam strives for accuracy. There must be no place in his diary for hyperbole or exaggeration, no matter how great the temptation to jazz up the story. Otherwise, as the years go by, his memories of that formative period in his life are liable to become mixed-up and confused, their credibility undermined by overstatement.

The matter-of-fact mood of the story reveals Sam to have the kind of calm, rational mindset one normally associates with scientists. Such a way of looking at the world is essential if he's to survive on his own in the wild. It's quite understandable, then, that he would adopt a suitably scientific approach in describing the natural world around him.

I would say that the tone of My Side of the Mountain is a fairly straightforward and neutral narration of the events.  That makes sense based on Sam's character.  The book is narrated from his first person view, so what the reader experiences is Sam's thoughts on everything.  Sam is not a character that is prone to "freaking out."  He is a thorough planner and goes about his business in a methodical, well planned out, analytical sort of fashion.  Because of Sam's tone, the mood of the novel follows the same kind of emotional backdrop.  Because Sam is calm through most of his trials, the feelings that the reader gets while reading the book stay calm as well.  Sure, there are times, when the mood switches to nervous or worried on the reader's part, but because Sam stays calm, those feelings never run away with the reader.