These two phrases have similar meanings and emphasize his children being destroyed. (See: [[rc://en/ta/man/translate/figs-parallelism]])
# May his children be cut off
This can be stated in active form. AT: "Cause his children to be cut off" or "Cause his children to die" (See: [[rc://en/ta/man/translate/figs-activepassive]])
# may their name be blotted out in the next generation
Here the idea of there being no one to carry on the family name is spoke of as "their name being blotted out." AT: "may there be no one to carry on his name" (See: [[rc://en/ta/man/translate/figs-metaphor]])