It is unclear whether the man's father has died and he will bury him immediately, or if the man wants to stay for a longer amount of time until his father dies so he can bury him then. The main point is the man wants to do something else first before he follows Jesus.
# first let me go
"before I do that, let me go"
# Leave the dead to bury their own dead
Jesus does not mean literally that dead people will bury other dead people. Possible meanings of "the dead" are 1) it is a metaphor for those who will soon die, or 2) it is a metaphor for those who do not follow Jesus and are spiritually dead. The main point is that a disciple must not let anything delay him from following Jesus. (See: [[rc://en/ta/man/translate/figs-metaphor]])