The deer scene in the beginning doesn't have anything to do with the plot, but it is symbolic of Josh's descent into madness.
Josh starts the film as a decent (albeit weird and mischievous) kid who is pushed to evil by the traumatic circumstances of murdering Daryl. At the end of the movie, Zach tries to appeal to Josh's humanity, but it doesn't work, and his reign of terror is only stopped by being apprehended. Despite this, the movie goes very far to show that Josh isn't evil, more traumatized and doubling down on the same behavior to regain some control of his life, with the implication that, as a child, he doesn't fully grasp just how bad his actions are. This is symbolized by the deer, which is essentially a stand-in for Josh himself, as a creature that is severely wounded, and likely to potentially harm others if left to its own devices (The deer snuck into the school, so if it was left alone and survived the night, it could potentially hurt or scare the children if they get too close). The deer, like Josh, is unlikely to grasp the full consequences of lashing out in its pain, which is pitiful but ultimately unhelpful in dealing with either. Essentially, both the deer and Josh are reduced to animals that need to be dealt with harshly, both for their own sake and the sake of others.
