The text is framed as an explanation by Jesus on the Mount of Olives concerning the life of Joseph, his stepfather. Agreeing with Mary's continued virginity, the text proclaims that Joseph had four sons (Judas, Justus, James, and Simon) and two daughters (Assia and Lydia) by a previous marriage. At age 90, after the death of his first wife, Joseph is given charge of the twelve year old virgin Mary. She lives in his household raising his youngest son James 'the less' along with Judas, until the time she is to be married at age 14½. Whoa whoa whoa, whoa. 14 and a half? That statutory, man.
So that's the background story, the text proceeds to paraphrase the Gospel of James, stopping at the point of Jesus' birth. The text states that Joseph was miraculously blessed with mental and physical youth, dying at the age of 111. His oldest sons (Justus and Simon) get married and have children, and likewise his two daughters get married and live in their own houses. Apparently unable to make it on their own and moved back in.
So let's dismiss this because New Testament apocrypha is like saying that the Timothy Zahn Star Wars books are absolute Star Wars cannon, and I'm sorry, I just can't believe it's nothing more than a guy trying to cash in on the geeks with too much cash and time on their hands, and not enough imagination of their own... and so we go to the Gospels for more accurate made up stuff.
Which leaves us hanging about what Jesus was like as a three year old, and better, as a teenager, and consequently nothing about Joseph, who simply vanishes from the scene never to be mentioned again, except for one brief reference: "Where did this man get this wisdom and these mighty works? Is not this the carpenter's son?" (Mt 13:54-55). The question asked has a type of parallel in each of the other Gospels (Mk 6:3; Lk 4:22; Jn 6:42), but none says "carpenter's son." Only Mark 6:3 uses the word "carpenter," but applied to Jesus, without mention of Joseph. It was the natural responsibility of a father to teach his trade to the son he was raising.
Besides the title "Son of David," Jesus also receives from Joseph the title "son of the carpenter," adding a concrete human dimension that is part of the mystery of the Incarnation. The son of the carpenter who grew up working at his father's side would necessarily also be known to the people of his hometown as "the carpenter."
The actual Greek word used for Joseph's profession occurs nowhere else in the New Testament apart from these two cases of Matthew and Mark. The word is broader than simply "carpenter," and may be applied to a builder or a worker of any hard material such as stone or metal, thus opening a wide range of possibilities for the type of work that Joseph did. Handyman just doesn't seem to cut it when it comes to writing the Gospels.
However, the passage containing the reference (Mt 13:53-58) indirectly may shed some light on Joseph's disappearance from the scene. It is the only time that this Gospel actually names Jesus as Joseph's "son," and it is the people of Nazareth, "his own country," who refer to him in this way. They are the first to take offense at his teaching, because they are all too aware of his ordinary human upbringing. This would furnish one explanation for Joseph's absence in Jesus' ministry, which begins immediately with a voice from Heaven declaring "This is my beloved Son" (Mt 3:17). It could only cause confusion in people's minds to have Jesus' human father present while he was being revealed as the unique Son of God. Kind of confusing that way.
The presence of a human father was necessary for Davidic descent, for protection, affection, and instruction. There are some who suggest that Joseph and Mary fled to Egypt to find a good moil... and hid in the hills to participate in the Dead Sea Scroll society and a hippie commune to write the song Kumbaya while waiting for King Herod to kick the bucket (Matthew 2:23)
From the absence of Joseph even when Mary is mentioned in the rest of Gospel, it may be concluded that he had died by the time of the beginning of Jesus' public ministry. No further narrative is available. The carpenter of Nazareth faithfully and unquestioningly fulfills all that God asks of him, and then just as quietly disappears. Maybe he beamed up?