It's used in the Bible (see quotes) and means that you make 'a clear and total break with the spiritually dead—that is, with the spiritually “dead” world you’re leaving behind. '
Let the dead bury the dead : Christian Psychology
Matthew 8:18-20: "When Jesus saw the crowd around him, he gave orders to cross to the other side of the lake. Then a teacher of the law came to him and said, 'Teacher, I will follow you hwerever you go.'
"Jesus replied, 'Foxes have holes and birds of the air have nests, but the Son of Man has no place to lay his head.'
"Another disciple said to him, 'Lord, first let me go and bury my father.'
"But Jesus told him, 'Follow me, and let the dead bury the dead.'"
Luke 9:59-62
And he said unto another, Follow me.
But he said, Lord, suffer me first to go and bury my father.
Jesus said unto him, Let the dead bury their dead: but go thou and preach the kingdom of God.
And another also said, Lord, I will follow thee; but let me first go bid them farewell, which are at home at my house.
And Jesus said unto him, No man, having put his hand to the plough, and looking back, is fit for the kingdom of God.