Early in the movie, we hear about Rustin Parr, a man who lived in the woods and had killed seven children; he was later executed by hanging. Supposedly under the psychological control of the Blair Witch, Parr had taken two children at a time into the basement and made one stand in the corner while he killed the other. According to the mythology of the Blair Witch, anyone who comes in contact with her will inevitably succumb to her control, and we may be able to assume that this is what happened to Josh. At the end of the movie, Mike was knocked down by someone or something, and when Heather finally arrived in the basement, she saw him standing motionless in a corner of the room. Josh was most likely used by the witch to lure Heather and Mike into the house, and then to physically attack them. What happened to him afterward is a tougher mystery to crack, though.
After Josh disappears, Heather comes across a stick bundle in the woods that contains Josh's necklace, a bloody piece of his shirt, and some sort of body part that many have thought looked like a tongue.