Exegesis:

aphes tous nekrous thapsai tous heautōn nekrous ‘let the dead bury their dead,’ i.e. ‘leave it to the dead to bury their dead.’ The meaning of tous nekrous is determined by the context. He who postpones the call of Jesus to the burying of the dead is, so to speak, dead himself. It is not advisable to press the figurative meaning of tous nekrous in such a way that it means ‘spiritually dead.’

su de apelthōn diaggelle tēn basileian tou theou ‘but you, go and proclaim the kingdom of God.’ apelthōn takes up apelthonti in v. 59.

diagellō ‘to proclaim (far and wide),’ ‘to preach,’ synonymous with kērussō, cf. 9.2.

Translation:

Leave the dead to bury their own dead is sometimes better slightly simplified, e.g. ‘the dead will take-care-of their dead’ (Tae’). The dead, or, as a simile, ‘those who are like the dead.’ Their own dead. The possessive may be taken to express the idea ‘the dead that are related to them, or, for whom (or, for whose funeral) they are responsible.’ Some versions have taken it to carry the meaning ‘those who are equally dead, or, as dead as they are,’ but this is not advisable. — The translator should avoid a rendering that will be understood to mean ‘let the dead take care of themselves.’

Proclaim, cf. on “preach” in 3.3.

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.