These are strong words, and they need to be handled carefully, especially by anyone who has recently buried a parent. Jesus is not saying funerals do not matter or that grief is unspiritual. Later in Matthew he rebukes the Pharisees for finding religious loopholes to avoid honoring their parents (Matthew 15:3-6). Jesus loves fathers and mothers. So what does he mean?
The dead cannot do anything; that is what makes them dead. Jesus must be using the word in two senses: let the spiritually dead take care of the business of death. Paul uses the same language when he says that before Christ we “were dead in our trespasses” (Ephesians 2:5). R. T. France captures it beautifully: a disciple’s business is with life, not with death. There are plenty of people in the world who do not know Jesus and who can handle the ordinary business of the world. But Jesus is offering this man life, and life is not something to put off.
Then comes the command itself: “Follow me.” Morris and Osborne both point out that it is a present tense command in Greek. It is not merely “start following me” but “keep following me.” Discipleship is not a one-time decision at the water’s edge. It is a lifetime of getting up every day and stepping back into the boat. This is why Jesus elsewhere speaks of taking up the cross daily (Luke 9:23). The question is not only whether you once said yes, but whether you are saying yes today.