If I may respectfully point to the book of A.T. Bradford who wrote "Joseph in John's gospel, Judas and Jewish jokes". He says the "who we know" is in the present tense in Greek suggesting very much that Joseph is still alive.
John 6:42 (NIV): They said, “Is this not Jesus, the son of Joseph, whose father and mother we know? How can he now say, ‘I came down from heaven’?”
Any thoughts from those who know Greek?
However, it's not just this - he suggests that John's gospel is littered with references to Joseph being alive!
For instance, John 8:14-19 when the Pharisees ask "Where is your father?" ... Jesus answers using double meaning (which I have come to learn there is a LOT of this in His teachings if you read Aramaic) - they are asking WHERE IS JOSEPH! Why? Because a Jewish man is not allowed to give legal testimony about himself until he is over 40.
Arguably, this is a similar situation to the man born blind. The Pharisees asked to see his parents who said: "He can answer for himself, he is of age!"
Jesus of course answers that they don't know his father. Our Lord is talking then of God, but the Pharisees often didn't get his meaning. He is making fun of them... again!
I don't have the knowledge yet to know if these answers are totally true but I would recommend reading the book - and please give your thoughts on the above.
A.T. Bradford does make some long reaches for inferences in his books and I don't agree with everything he said. But IF his paradigm of Jesus making fun of the Pharisees by confusing them about WHICH father he was talking about is correct: it makes a lot of sense of some of the things He said.